Wednesday, October 18, 2017

Number of the day: 586159

Properties of the number 586159:

586159 is a cyclic number.
586159 = 7 × 83737 is semiprime and squarefree.
586159 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 502416 totatives.
586159 has a semiprime digit sum 34 in base 10.
586159 has a Fibonacci digit sum 34 in base 10.
Reversing the decimal digits of 586159 results in a sphenic number.
586159 = 2930802 - 2930792 = 418722 - 418652 is the difference of 2 nonnegative squares in 2 ways.
586159 is the sum of 2 positive triangular numbers.
586159 is the difference of 2 positive pentagonal numbers in 2 ways.
586159 is not the sum of 3 positive squares.
5861592 = 2958552 + 5060162 is the sum of 2 positive squares in 1 way.
5861592 is the sum of 3 positive squares.
586159 is a proper divisor of 7972326 - 1.
586159 = '5861' + '59' is the concatenation of 2 prime numbers.
586159 = '58' + '6159' is the concatenation of 2 semiprime numbers.
586159 is an emirpimes in (at least) the following bases: 2, 5, 11, 14, 17, 18, 20, 24, 26, 30, 32, 33, 37, 41, 43, 44, 47, 51, 53, 54, 58, 59, 63, 65, 67, 73, 74, 78, 83, 86, 87, 91, 97, and 98.
586159 is palindromic in (at least) base -100.

The number 586159 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A148295: Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, -1), (-1, 0, 1), (-1, 1, 1), (0, 1, 0), (1, -1, 0)}

Tuesday, October 17, 2017

Number of the day: 94234

Properties of the number 94234:

94234 = 2 × 7 × 53 × 127 is the 85144th composite number and is squarefree.
94234 has 4 distinct prime factors, 16 divisors, 19 antidivisors and 39312 totatives.
94234 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 94234 results in a semiprime.
94234 is the difference of 2 positive pentagonal numbers in 5 ways.
94234 = 602 + 972 + 2852 is the sum of 3 positive squares.
942342 = 497842 + 800102 is the sum of 2 positive squares in 1 way.
942342 is the sum of 3 positive squares.
94234 is a proper divisor of 1073 - 1.
94234 is palindromic in (at least) the following bases: -51, and -87.
94234 in base 50 = bYY and consists of only the digits 'Y' and 'b'.

The number 94234 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A191490: Triangle generated by the recurrence T(n+1,k+1) = T(n,k+1) + n * T(n,k) + delta(n,k) with the initial values T(n,0) = 1 and T(0,k) = delta(k,0), where delta(n,k) is the Kronecker delta.
A231262: Number of (n+1)X(7+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order
A231263: T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order
A231265: Number of (3+1)X(n+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order
A238868: Number of partitions of n where the difference between consecutive parts is at most 8.

Monday, October 16, 2017

Number of the day: 467661421

Properties of the number 467661421:

467661421 = 192 × 43 × 47 × 641 is the 442922698th composite number and is not squarefree.
467661421 has 4 distinct prime factors, 24 divisors, 39 antidivisors and 422876160 totatives.
467661421 has an emirp digit sum 37 in base 10.
467661421 = 743 + 5413 + 6763 is the sum of 3 positive cubes in 1 way.
467661421 is the difference of 2 nonnegative squares in 12 ways.
467661421 is the sum of 2 positive triangular numbers.
467661421 is the difference of 2 positive pentagonal numbers in 10 ways.
467661421 = 5142 + 9152 + 216002 is the sum of 3 positive squares.
4676614212 = 1459162002 + 4443148292 is the sum of 2 positive squares in 1 way.
4676614212 is the sum of 3 positive squares.
467661421 is a proper divisor of 12837866 - 1.
467661421 = '467' + '661421' is the concatenation of 2 prime numbers.

Sunday, October 15, 2017

Number of the day: 6715453888

Properties of the number 6715453888:

6715453888 = 26 × 11 × 13 × 23 × 61 × 523 is the 6404212721th composite number and is not squarefree.
6715453888 has 6 distinct prime factors, 224 divisors, 65 antidivisors and 2645913600 totatives.
6715453888 has a semiprime digit sum 55 in base 10.
6715453888 has a Fibonacci digit sum 55 in base 10.
6715453888 has a triangular digit sum 55 in base 10.
6715453888 is the difference of 2 nonnegative squares in 80 ways.
6715453888 is the difference of 2 positive pentagonal numbers in 14 ways.
6715453888 is not the sum of 3 positive squares.
67154538882 = 25828668802 + 61988805122 = 14226938882 + 65630224002 = 36583557122 + 56314966402 = 12109834882 + 66053644802 is the sum of 2 positive squares in 4 ways.
67154538882 is the sum of 3 positive squares.
6715453888 is a proper divisor of 463660 - 1.
6715453888 is palindromic in (at least) base 7.

Saturday, October 14, 2017

Number of the day: 3265527765

Properties of the number 3265527765:

3265527765 = 3 × 5 × 217701851 is a sphenic number and squarefree.
3265527765 has 3 distinct prime factors, 8 divisors, 59 antidivisors and 1741614800 totatives.
3265527765 = 16327638832 - 16327638822 = 5442546292 - 5442546262 = 3265527792 - 3265527742 = 1088509332 - 1088509182 is the difference of 2 nonnegative squares in 4 ways.
3265527765 is the sum of 2 positive triangular numbers.
3265527765 is the difference of 2 positive pentagonal numbers in 2 ways.
3265527765 = 3052 + 4762 + 571422 is the sum of 3 positive squares.
32655277652 = 19593166592 + 26124222122 is the sum of 2 positive squares in 1 way.
32655277652 is the sum of 3 positive squares.
3265527765 is a proper divisor of 13214354037 - 1.

Thursday, October 12, 2017

Number of the day: 874427

Properties of the number 874427:

874427 is a cyclic number.
874427 is the 69406th prime.
874427 has 25 antidivisors and 874426 totatives.
Reversing the decimal digits of 874427 results in a sphenic number.
874427 = 4372142 - 4372132 is the difference of 2 nonnegative squares in 1 way.
874427 is the difference of 2 positive pentagonal numbers in 1 way.
874427 = 92 + 112 + 9352 is the sum of 3 positive squares.
8744272 is the sum of 3 positive squares.
874427 is a proper divisor of 4162459 - 1.
874427 = '87' + '4427' is the concatenation of 2 semiprime numbers.
874427 is an emirp in (at least) the following bases: 8, 11, 14, 19, 23, 27, 38, 47, 48, 54, 61, 69, 78, 81, 83, 88, 92, 93, and 97.

The number 874427 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A245466: a(n) = sigma_1(1) + sigma_2(2) + sigma_3(3) + ... + sigma_n-1(n-1) + sigma_n(n).

Wednesday, October 11, 2017

Number of the day: 2108

Properties of the number 2108:

2108 = 22 × 17 × 31 is the 1790th composite number and is not squarefree.
2108 has 3 distinct prime factors, 12 divisors, 9 antidivisors and 960 totatives.
2108 has a prime digit sum 11 in base 10.
2108 has sum of divisors equal to 4032 which is an oblong number.
2108 = 22 + … + 182 is the sum of at least 2 consecutive positive squares in 1 way.
2108 = 5282 - 5262 = 482 - 142 is the difference of 2 nonnegative squares in 2 ways.
2108 is the sum of 2 positive triangular numbers.
2108 is the difference of 2 positive pentagonal numbers in 2 ways.
2108 is not the sum of 3 positive squares.
21082 = 9922 + 18602 is the sum of 2 positive squares in 1 way.
21082 is the sum of 3 positive squares.
2108 is a proper divisor of 3732 - 1.
2108 is palindromic in (at least) the following bases: 5, 27, 43, 61, 67, -6, -39, and -49.
2108 in base 3 = 2220002 and consists of only the digits '0' and '2'.
2108 in base 14 = aa8 and consists of only the digits '8' and 'a'.
2108 in base 20 = 558 and consists of only the digits '5' and '8'.
2108 in base 26 = 332 and consists of only the digits '2' and '3'.
2108 in base 27 = 2o2 and consists of only the digits '2' and 'o'.
2108 in base 42 = 188 and consists of only the digits '1' and '8'.
2108 in base 43 = 161 and consists of only the digits '1' and '6'.
2108 in base 45 = 11c and consists of only the digits '1' and 'c'.

The number 2108 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A003106: Number of partitions of n into parts 5k+2 or 5k+3.
A028884: a(n) = (n + 3)^2 - 8.
A034327: Triangle of numbers of connected regular (k X n)-matrix matroids of dimension k.
A092945: Group the natural numbers so that the n-th group contains n numbers whose sum as well as the group product + 1 is prime. Sequence contains the last term of each group.
A105142: Positive integers n such that n^12 + 1 is semiprime.
A135789: Positive numbers of the form x^4 - 6 * x^2 * y^2 + y^4 (where x,y are integers).
A139570: 2n(n+3).
A229645: Cogrowth function of the group Baumslag-Solitar(3,3).
A238864: Number of partitions of n where the difference between consecutive parts is at most 4.
A260573: Numbers n such that (n^97+1)/(n+1) is prime.

Tuesday, October 10, 2017

Number of the day: 144655464

Properties of the number 144655464:

144655464 = 23 × 3 × 23 × 271 × 967 is the 136495097th composite number and is not squarefree.
144655464 has 5 distinct prime factors, 64 divisors, 19 antidivisors and 45904320 totatives.
144655464 has an emirpimes digit sum 39 in base 10.
144655464 is the difference of 2 nonnegative squares in 16 ways.
144655464 is the difference of 2 positive pentagonal numbers in 4 ways.
144655464 = 3522 + 4422 + 120142 is the sum of 3 positive squares.
1446554642 is the sum of 3 positive squares.
144655464 is a proper divisor of 1933270 - 1.

Monday, October 9, 2017

Number of the day: 9711868390

Properties of the number 9711868390:

9711868390 = 2 × 5 × 7 × 109 × 569 × 2237 is the 9269336931th composite number and is squarefree.
9711868390 has 6 distinct prime factors, 64 divisors, 39 antidivisors and 3291964416 totatives.
9711868390 is the difference of 2 positive pentagonal numbers in 15 ways.
9711868390 = 23612 + 25702 + 984872 is the sum of 3 positive squares.
97118683902 = 58271210342 + 77694947122 = 42928455362 + 87115937022 = 16818854782 + 95651267042 = 62185964962 + 74598555782 = 21710890322 + 94660847262 = 23461578562 + 94242204422 = 54202543362 + 80586121982 = 47347491942 + 84795364082 = 3864701822 + 97041758242 = 66693502822 + 70597559762 = 32788693282 + 91416302462 = 12114374162 + 96360161382 = 50190987422 + 83143872562 = 7147707142 + 96855299522 = 37442059622 + 89610997842 = 67077831942 + 70232494082 = 32289253362 + 91593901982 = 28048721822 + 92980148242 = 65764641182 + 71463632242 = 33981282722 + 90979729542 = 10853297842 + 96510334622 = 49099476582 + 83793079442 = 5880580862 + 96940484482 = 38610644382 + 89113730162 = 56643975782 + 78889154962 = 44729620322 + 86204987262 = 892331442 + 97114584422 = 53459826002 + 81080736102 = 48124597502 + 84356753602 = 10996266402 + 96494149502 = 57554885502 + 78227066402 = 15939296102 + 95801762002 = 29124938502 + 92648673602 = 52395014002 + 81772863902 = 49223562502 + 83720246402 = 9733533602 + 96629690502 = 61316816402 + 75314585502 = 39427796102 + 88755212002 = 4989638502 + 96990423602 = 43935676402 + 86612326502 is the sum of 2 positive squares in 40 ways.
97118683902 is the sum of 3 positive squares.
9711868390 is a proper divisor of 16214644 - 1.

Sunday, October 8, 2017

Number of the day: 9216

Properties of the number 9216:

9216 = 210 × 32 is the 8073th composite number and is not squarefree.
9216 has 2 distinct prime factors, 33 divisors, 4 antidivisors and 3072 totatives.
9216 = 962 is a perfect power.
9216 has sum of divisors equal to 26611 which is a sphenic number.
9216 = 962 is a perfect square.
9216 = 63 + 103 + 203 is the sum of 3 positive cubes in 1 way.
9216 = (95 × 96)/2 + (96 × 97)/2 is the sum of at least 2 consecutive triangular numbers in 1 way. In fact, it is the sum of 2 triangular numbers.
9216 is the difference of 2 nonnegative squares in 14 ways.
9216 is the difference of 2 positive pentagonal numbers in 1 way.
9216 is the sum of 3 positive squares.
92162 is the sum of 3 positive squares.
9216 is a proper divisor of 12794 - 1.
9216 = '921' + '6' is the concatenation of 2 semiprime numbers.
9216 is palindromic in (at least) the following bases: 31, 47, 95, -33, -49, and -97.
9216 in base 8 = 22000 and consists of only the digits '0' and '2'.
9216 in base 21 = kii and consists of only the digits 'i' and 'k'.
9216 in base 24 = g00 and consists of only the digits '0' and 'g'.
9216 in base 31 = 9i9 and consists of only the digits '9' and 'i'.
9216 in base 32 = 900 and consists of only the digits '0' and '9'.
9216 in base 46 = 4GG and consists of only the digits '4' and 'G'.
9216 in base 47 = 484 and consists of only the digits '4' and '8'.
9216 in base 48 = 400 and consists of only the digits '0' and '4'.

The number 9216 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005010: a(n) = 9*2^n.
A005179: Smallest number with exactly n divisors.
A007416: The minimal numbers: sequence A005179 arranged in increasing order.
A033845: Numbers n of the form 2^i*3^j, i and j >= 1.
A069273: 12-almost primes (generalization of semiprimes).
A106429: Smallest number beginning with 9 and having exactly n prime divisors counted with multiplicity.
A178715: a(n) = solution to the "Select All, Copy, Paste" problem: Given the ability to type a single letter, or to type individual "Select All", "Copy" or "Paste" command key strokes, what is the maximal number of letters of text that can be obtained with n key strokes?
A244120: Triangle read by rows: coefficients T(n,k) of a binomial decomposition of n^n as Sum(k=0..n)T(n,k)*binomial(n,k).
A244124: Triangle read by rows: coefficients T(n,k) of a binomial decomposition of 2^n-1 as Sum(k=0..n)T(n,k)*binomial(n,k).
A244125: Triangle read by rows: terms T(n,k) of a binomial decomposition of 2^n-1 as Sum(k=0..n)T(n,k).

Saturday, October 7, 2017

Number of the day: 9188

Properties of the number 9188:

9188 = 22 × 2297 is the 8048th composite number and is not squarefree.
9188 has 2 distinct prime factors, 6 divisors, 29 antidivisors and 4592 totatives.
9188 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 9188 results in a prime.
9188 = 22982 - 22962 is the difference of 2 nonnegative squares in 1 way.
9188 is the difference of 2 positive pentagonal numbers in 1 way.
9188 = 382 + 882 is the sum of 2 positive squares in 1 way.
9188 = 182 + 202 + 922 is the sum of 3 positive squares.
91882 = 63002 + 66882 is the sum of 2 positive squares in 1 way.
91882 is the sum of 3 positive squares.
9188 is a proper divisor of 65914 - 1.
9188 is palindromic in (at least) the following bases: 55, -34, and -36.
9188 in base 33 = 8ee and consists of only the digits '8' and 'e'.
9188 in base 54 = 388 and consists of only the digits '3' and '8'.
9188 in base 55 = 323 and consists of only the digits '2' and '3'.

The number 9188 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006758: Number of one-sided polyominoes with n cells.
A124057: Numbers n such that n, n+1, n+2 and n+3 are products of exactly 3 primes.
A143823: Number of subsets {x(1),x(2),...,x(k)} of {1,2,...,n} such that all differences |x(i)-x(j)| are distinct.
A153642: a(n) = 4*n^2 + 24*n + 8.
A231413: Number of (n+1)X(1+1) 0..2 arrays with no element equal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order
A231419: T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element equal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order
A240578: Number of partitions of n such that the number of odd parts is a part and the number of even parts is not a part.
A280362: T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal and vertical neighbors and with new values introduced in order 0 sequentially upwards.
A281080: T(n,k)=Number of nXk 0..1 arrays with no element equal to more than two of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
A281605: T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal, diagonal or antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Friday, October 6, 2017

Number of the day: 198445

Richard Dedekind was born on this day 186 years ago.

Properties of the number 198445:

198445 = 5 × 13 × 43 × 71 is the 180585th composite number and is squarefree.
198445 has 4 distinct prime factors, 16 divisors, 39 antidivisors and 141120 totatives.
198445 has an emirp digit sum 31 in base 10.
Reversing the decimal digits of 198445 results in a semiprime.
198445 = 992232 - 992222 = 198472 - 198422 = 76392 - 76262 = 23292 - 22862 = 15592 - 14942 = 14332 - 13622 = 5692 - 3542 = 4572 - 1022 is the difference of 2 nonnegative squares in 8 ways.
198445 is the sum of 2 positive triangular numbers.
198445 is the difference of 2 positive pentagonal numbers in 7 ways.
198445 = 612 + 902 + 4322 is the sum of 3 positive squares.
1984452 = 1190672 + 1587562 = 488482 + 1923392 = 1007492 + 1709682 = 763252 + 1831802 is the sum of 2 positive squares in 4 ways.
1984452 is the sum of 3 positive squares.
198445 is a proper divisor of 85312 - 1.

Thursday, October 5, 2017

Number of the day: 709383

Properties of the number 709383:

709383 = 3 × 236461 is semiprime and squarefree.
709383 has 2 distinct prime factors, 4 divisors, 19 antidivisors and 472920 totatives.
709383 has a sphenic digit sum 30 in base 10.
709383 has an oblong digit sum 30 in base 10.
Reversing the decimal digits of 709383 results in a sphenic number.
709383 = 3546922 - 3546912 = 1182322 - 1182292 is the difference of 2 nonnegative squares in 2 ways.
709383 is the difference of 2 positive pentagonal numbers in 1 way.
709383 is not the sum of 3 positive squares.
7093832 = 2220332 + 6737402 is the sum of 2 positive squares in 1 way.
7093832 is the sum of 3 positive squares.
709383 is a proper divisor of 7984 - 1.
709383 = '709' + '383' is the concatenation of 2 prime numbers.
709383 is an emirpimes in (at least) the following bases: 2, 3, 9, 15, 19, 27, 29, 32, 33, 36, 47, 51, 55, 60, 63, 71, 72, 73, 78, 84, 87, 90, and 93.
709383 in base 60 = 3H33 and consists of only the digits '3' and 'H'.

Wednesday, October 4, 2017

Number of the day: 3094

Properties of the number 3094:

3094 = 2 × 7 × 13 × 17 is the 2651th composite number and is squarefree.
3094 has 4 distinct prime factors, 16 divisors, 11 antidivisors and 1152 totatives.
Reversing the decimal digits of 3094 results in a prime.
3094 = (15 × 16)/2 + … + (27 × 28)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
3094 is the sum of 2 positive triangular numbers.
3094 is the difference of 2 positive pentagonal numbers in 5 ways.
3094 = 132 + 302 + 452 is the sum of 3 positive squares.
30942 = 14562 + 27302 = 2942 + 30802 = 19602 + 23942 = 11902 + 28562 is the sum of 2 positive squares in 4 ways.
30942 is the sum of 3 positive squares.
3094 is a proper divisor of 8832 - 1.
3094 = '309' + '4' is the concatenation of 2 semiprime numbers.
3094 is palindromic in (at least) the following bases: 21, 90, -21, and -30.
3094 in base 5 = 44334 and consists of only the digits '3' and '4'.
3094 in base 18 = 99g and consists of only the digits '9' and 'g'.
3094 in base 20 = 7ee and consists of only the digits '7' and 'e'.
3094 in base 21 = 707 and consists of only the digits '0' and '7'.
3094 in base 55 = 11E and consists of only the digits '1' and 'E'.

The number 3094 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000638: Number of permutation groups of degree n; also number of conjugacy classes of subgroups of symmetric group S_n; also number of molecular species of degree n.
A002865: Number of partitions of n that do not contain 1 as a part.
A057809: Numbers n such that pi(n) divides n.
A105078: Positive integers n such that n^10 + 1 is semiprime.
A105142: Positive integers n such that n^12 + 1 is semiprime.
A155596: 5^n-2^n+1^n
A182746: Bisection (even part) of number of partitions that do not contain 1 as a part A002865.
A187219: Number of partitions of n that do not contain parts less than the smallest part of the partitions of n-1.
A255872: Smallest Rhonda number to base b = n-th composite number, cf. A002808.
A285332: a(0) = 1, a(1) = 2, a(2n) = A019565(a(n)), a(2n+1) = A065642(a(n)).

Tuesday, October 3, 2017

Number of the day: 83409

Properties of the number 83409:

83409 is a cyclic number.
83409 = 3 × 27803 is semiprime and squarefree.
83409 has 2 distinct prime factors, 4 divisors, 7 antidivisors and 55604 totatives.
Reversing the decimal digits of 83409 results in a sphenic number.
83409 = 417052 - 417042 = 139032 - 139002 is the difference of 2 nonnegative squares in 2 ways.
83409 is the difference of 2 positive pentagonal numbers in 1 way.
83409 = 132 + 382 + 2862 is the sum of 3 positive squares.
834092 is the sum of 3 positive squares.
83409 is a proper divisor of 713901 - 1.
83409 = '83' + '409' is the concatenation of 2 prime numbers.
83409 is an emirpimes in (at least) the following bases: 2, 6, 11, 15, 19, 27, 28, 31, 33, 36, 39, 40, 41, 44, 45, 49, 51, 55, 59, 66, 69, 71, 75, 78, 81, 83, 85, 92, 94, 97, and 99.
83409 is palindromic in (at least) the following bases: 61, and -100.
83409 in base 22 = 7i77 and consists of only the digits '7' and 'i'.
83409 in base 61 = MPM and consists of only the digits 'M' and 'P'.

The number 83409 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A277217: Numbers n for which the sum of digits of sigma(n) = the product of digits of sigma(n).

Monday, October 2, 2017

Number of the day: 78968

Properties of the number 78968:

78968 = 23 × 9871 is the 71224th composite number and is not squarefree.
78968 has 2 distinct prime factors, 8 divisors, 9 antidivisors and 39480 totatives.
78968 has a semiprime digit sum 38 in base 10.
Reversing the decimal digits of 78968 results in a semiprime.
78968 = 197432 - 197412 = 98732 - 98692 is the difference of 2 nonnegative squares in 2 ways.
78968 = 282 + 302 + 2782 is the sum of 3 positive squares.
789682 is the sum of 3 positive squares.
78968 is a proper divisor of 97747 - 1.
78968 is palindromic in (at least) the following bases: 45, 94, and -71.
78968 in base 45 = cic and consists of only the digits 'c' and 'i'.
78968 in base 47 = ZZ8 and consists of only the digits '8' and 'Z'.

Sunday, October 1, 2017

Number of the day: 23782

Properties of the number 23782:

23782 = 2 × 11 × 23 × 47 is the 21136th composite number and is squarefree.
23782 has 4 distinct prime factors, 16 divisors, 29 antidivisors and 10120 totatives.
23782 has a semiprime digit sum 22 in base 10.
23782 is the difference of 2 positive pentagonal numbers in 2 ways.
23782 is the difference of 2 positive pentagonal pyramidal numbers in 1 way.
23782 = 72 + 182 + 1532 is the sum of 3 positive squares.
237822 is the sum of 3 positive squares.
23782 is a proper divisor of 65922 - 1.
23782 = '237' + '82' is the concatenation of 2 semiprime numbers.
23782 = '2' + '3782' is the concatenation of 2 oblong numbers.
23782 is palindromic in (at least) the following bases: 79, -9, and -33.
23782 in base 44 = CCM and consists of only the digits 'C' and 'M'.
23782 in base 46 = BB0 and consists of only the digits '0' and 'B'.
23782 in base 54 = 88M and consists of only the digits '8' and 'M'.

The number 23782 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A004801: Sum of 12 positive 9th powers.
A128401: Numbers n such that n^2 divides 21^n-1.
A163815: a(n) = n*(2*n^2 + 5*n + 3).
A225708: Composite squarefree numbers n such that p(i)-8 divides n+8, where p(i) are the prime factors of n.
A238590: Number of partitions p of n such that 3*min(p) is a part of p.
A257368: Numbers n such that the decimal expansions of both n and n^2 have 2 as smallest digit and 8 as largest digit.
A290473: Numbers k such that 3*10^k + 13 is prime.

Saturday, September 30, 2017

Number of the day: 955738977518

Properties of the number 955738977518:

955738977518 = 2 × 132 × 17 × 2671 × 62273 is composite and not squarefree.
955738977518 has 5 distinct prime factors, 48 divisors, 55 antidivisors and 415000535040 totatives.
955738977518 has a semiprime digit sum 74 in base 10.
Reversing the decimal digits of 955738977518 results in a semiprime.
955738977518 is the difference of 2 positive pentagonal numbers in 11 ways.
955738977518 = 3872 + 27822 + 9776152 is the sum of 3 positive squares.
9557389775182 = 4497595188322 + 8432990978102 = 1427856288822 + 9450128344802 = 4078841364002 + 8643306800182 = 4952685937682 + 8174019899502 = 908168259182 + 9514143667602 = 6409651906322 + 7089433105302 = 6054455061202 + 7395084396182 = 440735566702 + 9547222186322 = 2316643558322 + 9272370890902 = 3189896719182 + 9009342830402 = 2820976863682 + 9131581946702 = 5640369931202 + 7715563903822 = 3265175702402 + 8982334159182 = 2744464519502 + 9154868312322 = 5704736704182 + 7668094838402 = 3675919144302 + 8822205946322 = 2319371397202 + 9271688931182 = 4881694764182 + 8216614603602 = 5706992417102 + 7666416168322 = 6729759664182 + 6786312266402 = 1345943396322 + 9462142235702 = 1425075991502 + 9450548012322 is the sum of 2 positive squares in 22 ways.
9557389775182 is the sum of 3 positive squares.
955738977518 is a proper divisor of 257194376 - 1.
955738977518 = '955' + '738977518' is the concatenation of 2 semiprime numbers.

Friday, September 29, 2017

Number of the day: 976985

Properties of the number 976985:

976985 = 5 × 37 × 5281 is a sphenic number and squarefree.
976985 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 760320 totatives.
Reversing the decimal digits of 976985 results in a semiprime.
976985 = 4884932 - 4884922 = 977012 - 976962 = 132212 - 131842 = 27332 - 25482 is the difference of 2 nonnegative squares in 4 ways.
976985 is the difference of 2 positive pentagonal numbers in 4 ways.
976985 = 6162 + 7732 = 3322 + 9312 = 2932 + 9442 = 292 + 9882 is the sum of 2 positive squares in 4 ways.
976985 = 422 + 552 + 9862 is the sum of 3 positive squares.
9769852 = 6310252 + 7458602 = 3550152 + 9102002 = 406252 + 9761402 = 5531842 + 8052872 = 2621082 + 9411692 = 573042 + 9753032 = 6181842 + 7565372 = 5151512 + 8301322 = 2180732 + 9523362 = 5861912 + 7815882 = 5492242 + 8079932 = 3010172 + 9294562 = 3168602 + 9241752 is the sum of 2 positive squares in 13 ways.
9769852 is the sum of 3 positive squares.
976985 is a proper divisor of 115312 - 1.

Thursday, September 28, 2017

Number of the day: 829888

Properties of the number 829888:

829888 = 26 × 12967 is the 763731th composite number and is not squarefree.
829888 has 2 distinct prime factors, 14 divisors, 25 antidivisors and 414912 totatives.
829888 has a prime digit sum 43 in base 10.
829888 = 2074732 - 2074712 = 1037382 - 1037342 = 518722 - 518642 = 259422 - 259262 = 129832 - 129512 is the difference of 2 nonnegative squares in 5 ways.
829888 is the sum of 2 positive triangular numbers.
829888 is the difference of 2 positive pentagonal numbers in 1 way.
829888 is not the sum of 3 positive squares.
8298882 is the sum of 3 positive squares.
829888 is a proper divisor of 1932161 - 1.

Wednesday, September 27, 2017

Number of the day: 58200

Properties of the number 58200:

58200 = 23 × 3 × 52 × 97 is the 52305th composite number and is not squarefree.
58200 has 4 distinct prime factors, 48 divisors, 19 antidivisors and 15360 totatives.
58200 has an emirpimes digit sum 15 in base 10.
58200 has a triangular digit sum 15 in base 10.
58200 is the difference of 2 nonnegative squares in 12 ways.
58200 is the sum of 2 positive triangular numbers.
58200 is the difference of 2 positive pentagonal numbers in 1 way.
58200 = 202 + 342 + 2382 is the sum of 3 positive squares.
582002 = 390002 + 432002 = 52802 + 579602 = 111602 + 571202 = 305522 + 495362 = 253442 + 523922 = 349202 + 465602 = 162962 + 558722 is the sum of 2 positive squares in 7 ways.
582002 is the sum of 3 positive squares.
58200 is a proper divisor of 1934 - 1.
58200 in base 5 = 3330300 and consists of only the digits '0' and '3'.
58200 in base 22 = 5a5a and consists of only the digits '5' and 'a'.
58200 in base 58 = HHQ and consists of only the digits 'H' and 'Q'.

The number 58200 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A015578: Expansion of x/(1-8x-11x^2).
A018211: Alkane (or paraffin) numbers l(10,n).

Tuesday, September 26, 2017

Number of the day: 5370

Properties of the number 5370:

5370 = 2 × 3 × 5 × 179 is the 4661th composite number and is squarefree.
5370 has 4 distinct prime factors, 16 divisors, 9 antidivisors and 1424 totatives.
5370 has an emirpimes digit sum 15 in base 10.
5370 has a triangular digit sum 15 in base 10.
5370 is the sum of 2 positive triangular numbers.
5370 is the difference of 2 positive pentagonal numbers in 1 way.
5370 is the difference of 2 positive pentagonal pyramidal numbers in 2 ways.
5370 = (60 × (3 × 60-1))/2 is a pentagonal number.
5370 = 42 + 52 + 732 is the sum of 3 positive squares.
53702 = 32222 + 42962 is the sum of 2 positive squares in 1 way.
53702 is the sum of 3 positive squares.
5370 is a proper divisor of 3592 - 1.
5370 is palindromic in (at least) the following bases: 44, 59, -23, -61, and -91.
5370 in base 22 = b22 and consists of only the digits '2' and 'b'.
5370 in base 43 = 2cc and consists of only the digits '2' and 'c'.
5370 in base 44 = 2Y2 and consists of only the digits '2' and 'Y'.
5370 in base 58 = 1YY and consists of only the digits '1' and 'Y'.
5370 in base 59 = 1W1 and consists of only the digits '1' and 'W'.

The number 5370 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002625: Expansion of 1/((1-x)^3*(1-x^2)^2*(1-x^3)).
A014633: Even pentagonal numbers.
A049452: Pentagonal numbers with even index.
A196485: T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,0,2,1,4 for x=0,1,2,3,4
A222604: Number of nX1 0..3 arrays with exactly floor(nX1/2) elements equal to at least one king-move neighbor, with new values introduced in row major 0..3 order
A222747: T(n,k)=Number of nXk 0..3 arrays with exactly floor(nXk/2) elements equal to at least one horizontal or antidiagonal neighbor, with new values introduced in row major 0..3 order
A226253: Number of ways of writing n as the sum of 9 triangular numbers.
A232696: E.g.f. A(x) satisfies: A'(x) = A(x/A'(x)) with A(0)=1.
A246479: T(n,k)=Number of length n+3 0..k arrays with no pair in any consecutive four terms totalling exactly k
A263373: T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with each row and column divisible by 7, read as a base-3 number with top and left being the most significant digits.

Monday, September 25, 2017

Number of the day: 672028146

Properties of the number 672028146:

672028146 = 2 × 32 × 37334897 is the 637149995th composite number and is not squarefree.
672028146 has 3 distinct prime factors, 12 divisors, 7 antidivisors and 224009376 totatives.
672028146 has a triangular digit sum 36 in base 10.
672028146 is the sum of 2 positive triangular numbers.
672028146 is the difference of 2 positive pentagonal numbers in 2 ways.
672028146 = 48752 + 254612 is the sum of 2 positive squares in 1 way.
672028146 = 9292 + 13242 + 258732 is the sum of 3 positive squares.
6720281462 = 2482447502 + 6244968962 is the sum of 2 positive squares in 1 way.
6720281462 is the sum of 3 positive squares.
672028146 is a proper divisor of 1789264162 - 1.
672028146 = '67202' + '8146' is the concatenation of 2 semiprime numbers.

Sunday, September 24, 2017

Number of the day: 3930

Gerolamo Cardano was born on this day 516 years ago.

Properties of the number 3930:

3930 = 2 × 3 × 5 × 131 is the 3384th composite number and is squarefree.
3930 has 4 distinct prime factors, 16 divisors, 11 antidivisors and 1040 totatives.
3930 has an emirpimes digit sum 15 in base 10.
3930 has a triangular digit sum 15 in base 10.
3930 = 262 + … + 302 is the sum of at least 2 consecutive positive squares in 1 way.
3930 is the difference of 2 positive pentagonal numbers in 1 way.
3930 = 72 + 202 + 592 is the sum of 3 positive squares.
39302 = 23582 + 31442 is the sum of 2 positive squares in 1 way.
39302 is the sum of 3 positive squares.
3930 is a proper divisor of 10492 - 1.
3930 is palindromic in (at least) the following bases: 33, and -20.
3930 in base 19 = agg and consists of only the digits 'a' and 'g'.
3930 in base 32 = 3qq and consists of only the digits '3' and 'q'.
3930 in base 33 = 3k3 and consists of only the digits '3' and 'k'.
3930 in base 62 = 11O and consists of only the digits '1' and 'O'.

The number 3930 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A027578: Sums of five consecutive squares: a(n) = n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2.
A075386: Sum of terms of n-th group in A075383.
A076409: Sum of the quadratic residues of prime(n).
A113744: Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 7 multiples of n-1, n-2, ..., 1, for n>=1.
A138989: a(n) = Frobenius number for 3 successive primes = F[p(n),p(n+1),p(n+2)].
A211978: Total number of parts in all partitions of n plus the sum of largest parts of all partitions of n.
A251829: T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and column sum not 3 or 6 and every diagonal and antidiagonal sum 3 or 6
A256874: Numbers divisible by prime(d) for each digit d in their base 4 representation, none of which may be zero.
A282035: Sum of quadratic residues of (n-th prime == 3 mod 4).
A284949: Triangle read by rows: T(n,k) = number of reversible string structures of length n using exactly k different symbols.

Saturday, September 23, 2017

Number of the day: 378574

Properties of the number 378574:

378574 = 2 × 72 × 3863 is the 346389th composite number and is not squarefree.
378574 has 3 distinct prime factors, 12 divisors, 13 antidivisors and 162204 totatives.
378574 has a semiprime digit sum 34 in base 10.
378574 has a Fibonacci digit sum 34 in base 10.
Reversing the decimal digits of 378574 results in a semiprime.
378574 = (99 × 100)/2 + … + (147 × 148)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
378574 is the difference of 2 positive pentagonal numbers in 6 ways.
378574 = 52 + 182 + 6152 is the sum of 3 positive squares.
3785742 is the sum of 3 positive squares.
378574 is a proper divisor of 4911931 - 1.
378574 = '3785' + '74' is the concatenation of 2 semiprime numbers.

Thursday, September 21, 2017

Number of the day: 1482

Properties of the number 1482:

1482 = 2 × 3 × 13 × 19 is the 1247th composite number and is squarefree.
1482 has 4 distinct prime factors, 16 divisors, 9 antidivisors and 432 totatives.
1482 has an emirpimes digit sum 15 in base 10.
1482 has a triangular digit sum 15 in base 10.
Reversing the decimal digits of 1482 results in a semiprime.
1482 = 42 + … + 162 is the sum of at least 2 consecutive positive squares in 1 way.
1482 is the sum of 2 positive triangular numbers.
1482 = 38 × 39 is an oblong number.
1482 = 72 + 82 + 372 is the sum of 3 positive squares.
14822 = 5702 + 13682 is the sum of 2 positive squares in 1 way.
14822 is the sum of 3 positive squares.
1482 is a proper divisor of 5712 - 1.
1482 = '14' + '82' is the concatenation of 2 semiprime numbers.
1482 is palindromic in (at least) the following bases: 5, 56, 77, and -37.
1482 in base 3 = 2000220 and consists of only the digits '0' and '2'.
1482 in base 14 = 77c and consists of only the digits '7' and 'c'.
1482 in base 38 = 110 and consists of only the digits '0' and '1'.

The number 1482 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002378: Oblong (or promic, pronic, or heteromecic) numbers: a(n) = n*(n+1).
A002943: a(n) = 2*n*(2*n+1).
A014574: Average of twin prime pairs.
A033537: a(n) = n*(2*n+5).
A045896: Denominator of n/((n+1)(n+2)) = A026741/A045896.
A046386: Products of four distinct primes.
A097024: Numbers in the 5-cycle-attractor if the f[x]=A063919[x] function is iterated; f[x] is the sum of unitary proper divisors.
A124178: Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + n^13 + n^15 + n^17 + n^19 is prime.
A170758: G.f.: (1+x)/(1-38*x).
A177905: Numbers n such that n^3 divides 5^(n^2)-1.

Wednesday, September 20, 2017

Number of the day: 129

Properties of the number 129:

129 = 3 × 43 is semiprime and squarefree.
129 has 2 distinct prime factors, 4 divisors, 5 antidivisors and 84 totatives.
129 has an oblong digit sum 12 in base 10.
Reversing the decimal digits of 129 results in an emirpimes.
129 = 13 + 43 + 43 is the sum of 3 positive cubes in 1 way.
129 = 652 - 642 = 232 - 202 is the difference of 2 nonnegative squares in 2 ways.
129 is the difference of 2 positive pentagonal numbers in 1 way.
129 = 22 + 52 + 102 is the sum of 3 positive squares.
1292 is the sum of 3 positive squares.
129 is a proper divisor of 1732 - 1.
129 is an emirpimes in (at least) the following bases: 3, 5, 7, 9, 10, 12, 14, 15, 17, 19, 21, 23, 24, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 45, 51, 55, 60, 69, 71, 72, 78, 80, 84, 89, 91, 93, 94, 98, and 100.
129 is palindromic in (at least) the following bases: 2, 6, 42, -7, -16, -32, and -64.
129 in base 6 = 333 and consists of only the digit '3'.

The number 129 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000051: a(n) = 2^n + 1.
A000930: Narayana's cows sequence: a(0) = a(1) = a(2) = 1; thereafter a(n) = a(n-1) + a(n-3).
A000959: Lucky numbers.
A001358: Semiprimes (or biprimes): products of two primes.
A001969: Evil numbers: numbers with an even number of 1's in their binary expansion.
A005408: The odd numbers: a(n) = 2*n + 1.
A006881: Squarefree semiprimes: Numbers that are the product of two distinct primes.
A007504: Sum of first n primes.
A008585: a(n) = 3*n.
A016813: a(n) = 4n + 1.

Tuesday, September 19, 2017

Number of the day: 962716

Ky Fan was born on this day 103 years ago.

Properties of the number 962716:

962716 = 22 × 229 × 1051 is the 886891th composite number and is not squarefree.
962716 has 3 distinct prime factors, 12 divisors, 13 antidivisors and 478800 totatives.
962716 has an emirp digit sum 31 in base 10.
962716 has sum of divisors equal to 1693720 which is a triangular number.
Reversing the decimal digits of 962716 results in a prime.
962716 = 2406802 - 2406782 = 12802 - 8222 is the difference of 2 nonnegative squares in 2 ways.
962716 is the difference of 2 positive pentagonal numbers in 2 ways.
962716 is not the sum of 3 positive squares.
9627162 = 2522402 + 9290842 is the sum of 2 positive squares in 1 way.
9627162 is the sum of 3 positive squares.
962716 is a proper divisor of 137370 - 1.

Monday, September 18, 2017

Number of the day: 19499565

Adrien-Marie Legendre was born on this day 265 years ago.

Properties of the number 19499565:

19499565 = 3 × 5 × 61 × 101 × 211 is the 18258760th composite number and is squarefree.
19499565 has 5 distinct prime factors, 32 divisors, 35 antidivisors and 10080000 totatives.
19499565 is the difference of 2 nonnegative squares in 16 ways.
19499565 is the difference of 2 positive pentagonal numbers in 7 ways.
19499565 = 1002 + 2772 + 44062 is the sum of 3 positive squares.
194995652 = 83790212 + 176075282 = 50665322 + 188298512 = 114167882 + 158079092 = 38613002 + 191134352 = 3513152 + 194964002 = 72446852 + 181038002 = 129739682 + 145571012 = 101362292 + 166580282 = 119788922 + 153863312 = 116997392 + 155996522 = 86948882 + 174537092 = 132341312 + 143209922 = 35163152 + 191799002 is the sum of 2 positive squares in 13 ways.
194995652 is the sum of 3 positive squares.
19499565 is a proper divisor of 10760 - 1.
19499565 = '194' + '99565' is the concatenation of 2 semiprime numbers.

Sunday, September 17, 2017

Number of the day: 85501

Bernhard Riemann was born on this day 191 years ago.

Properties of the number 85501:

85501 is a cyclic number.
85501 = 13 × 6577 is semiprime and squarefree.
85501 has 2 distinct prime factors, 4 divisors, 19 antidivisors and 78912 totatives.
85501 has a prime digit sum 19 in base 10.
Reversing the decimal digits of 85501 results in an emirpimes.
85501 = 427512 - 427502 = 32952 - 32822 is the difference of 2 nonnegative squares in 2 ways.
85501 is the sum of 2 positive triangular numbers.
85501 is the difference of 2 positive pentagonal numbers in 2 ways.
85501 = 1742 + 2352 = 1502 + 2512 is the sum of 2 positive squares in 2 ways.
85501 = 212 + 462 + 2882 is the sum of 3 positive squares.
855012 = 249492 + 817802 = 84242 + 850852 = 405012 + 753002 = 328852 + 789242 is the sum of 2 positive squares in 4 ways.
855012 is the sum of 3 positive squares.
85501 is a proper divisor of 35312 - 1.
85501 = '85' + '501' is the concatenation of 2 semiprime numbers.
85501 is an emirpimes in (at least) the following bases: 2, 8, 9, 10, 13, 21, 27, 28, 31, 35, 36, 37, 38, 39, 40, 42, 44, 45, 49, 53, 54, 58, 66, 71, 78, 80, 81, 83, 85, 86, 87, 88, 89, and 97.
85501 is palindromic in (at least) the following bases: -14, and -71.
85501 in base 14 = 23233 and consists of only the digits '2' and '3'.

Saturday, September 16, 2017

Number of the day: 11292

Properties of the number 11292:

11292 = 22 × 3 × 941 is the 9926th composite number and is not squarefree.
11292 has 3 distinct prime factors, 12 divisors, 7 antidivisors and 3760 totatives.
11292 has an emirpimes digit sum 15 in base 10.
11292 has a triangular digit sum 15 in base 10.
11292 has a triangular digit product 36 in base 10.
11292 = 342 + … + 412 is the sum of at least 2 consecutive positive squares in 1 way.
11292 = 28242 - 28222 = 9442 - 9382 is the difference of 2 nonnegative squares in 2 ways.
11292 is the sum of 2 positive triangular numbers.
11292 is the difference of 2 positive pentagonal numbers in 1 way.
11292 is not the sum of 3 positive squares.
112922 = 69602 + 88922 is the sum of 2 positive squares in 1 way.
112922 is the sum of 3 positive squares.
11292 is a proper divisor of 974 - 1.
11292 = '1129' + '2' is the concatenation of 2 prime numbers.
11292 is palindromic in (at least) the following bases: 30, -23, and -71.
11292 in base 30 = cgc and consists of only the digits 'c' and 'g'.
11292 in base 47 = 55C and consists of only the digits '5' and 'C'.

The number 11292 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006550: n+8*C(n,2)+30*C(n,3)+62*C(n,4)+75*C(n,5)+30*C(n,6).
A034997: Number of Generalized Retarded Functions in Quantum Field Theory.
A101713: Indices of primes in sequence defined by A(0) = 43, A(n) = 10*A(n-1) - 27 for n > 0.
A137200: Number of ways to tile an n X 1 strip with 1 X 1 squares and 2 X 1 dominoes with the restriction that no three consecutive tiles are of the same type.
A212584: Nonnegative walks of length n on the x-axis starting at the origin using steps {1,-1} and visiting no point more than twice.
A213754: Principal diagonal of the convolution array A213753.
A227333: T(n,k)=Number of nXk 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X(k+1) binary array having two adjacent 1s and two adjacent 0s, with rows and columns of the latter in lexicographically nondecreasing order
A271580: Magic sums of 4 X 4 magic squares composed of squares.
A289191: Number of polygonal tiles with n sides with two exits per side and n edges connecting pairs of exits, with no edges between exits on the same side and non-isomorphic under rotational symmetry.
A289343: a(n) = A289191(prime(n)).

Friday, September 15, 2017

Number of the day: 894518

Properties of the number 894518:

894518 = 2 × 447259 is semiprime and squarefree.
894518 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 447258 totatives.
894518 has a semiprime digit sum 35 in base 10.
Reversing the decimal digits of 894518 results in a sphenic number.
894518 = 72 + 382 + 9452 is the sum of 3 positive squares.
8945182 is the sum of 3 positive squares.
894518 is a proper divisor of 853926 - 1.
894518 = '894' + '518' is the concatenation of 2 sphenic numbers.
894518 is an emirpimes in (at least) the following bases: 2, 7, 8, 16, 26, 27, 30, 32, 36, 38, 40, 41, 43, 52, 62, 67, 70, 75, 76, 82, 84, 87, 88, 90, 91, 98, 99, and 100.

Thursday, September 14, 2017

Number of the day: 8347

Properties of the number 8347:

8347 is a cyclic number.
8347 = 17 × 491 is semiprime and squarefree.
8347 has 2 distinct prime factors, 4 divisors, 25 antidivisors and 7840 totatives.
8347 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 8347 results in an emirpimes.
8347 = 41742 - 41732 = 2542 - 2372 is the difference of 2 nonnegative squares in 2 ways.
8347 is the sum of 2 positive triangular numbers.
8347 is the difference of 2 positive pentagonal numbers in 2 ways.
8347 = 72 + 272 + 872 is the sum of 3 positive squares.
83472 = 39282 + 73652 is the sum of 2 positive squares in 1 way.
83472 is the sum of 3 positive squares.
8347 is a proper divisor of 10110 - 1.
8347 = '83' + '47' is the concatenation of 2 prime numbers.
8347 is an emirpimes in (at least) the following bases: 5, 6, 8, 9, 10, 21, 26, 28, 33, 34, 35, 37, 38, 43, 45, 50, 54, 55, 56, 57, 59, 60, 62, 66, 68, 70, 73, 79, 82, 84, 88, 90, 98, and 99.
8347 is palindromic in (at least) the following bases: 31, 78, -43, and -56.
8347 in base 7 = 33223 and consists of only the digits '2' and '3'.
8347 in base 31 = 8l8 and consists of only the digits '8' and 'l'.
8347 in base 34 = 77h and consists of only the digits '7' and 'h'.

The number 8347 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005676: Sum C(n-k,4*k), k = 0..n.
A007042: Diagonal of partition triangle A047812.
A009962: Coordination sequence for sigma-CrFe, Position Xa.
A031899: Lucky numbers with size of gaps equal to 16 (upper terms).
A035107: First differences give (essentially) A028242.
A128034: a(0)=a(1)=1. a(n) = the multiple of n which is > a(n-1)+a(n-2) and is <= a(n-1)+a(n-2)+n.
A240012: Number of partitions of n, where the difference between the number of odd parts and the number of even parts is 3.
A268325: Number of length-(n+1) 0..6 arrays with new values introduced in sequential order, and with new repeated values introduced in sequential order, both starting with zero.
A272223: Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 441", based on the 5-celled von Neumann neighborhood.
A279754: Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 197", based on the 5-celled von Neumann neighborhood.

Wednesday, September 13, 2017

Number of the day: 4057

Properties of the number 4057:

4057 is a cyclic number.
4057 is the 560th prime.
4057 has 13 antidivisors and 4056 totatives.
4057 has sum of divisors equal to 4058 which is semiprime.
4057 = 20292 - 20282 is the difference of 2 nonnegative squares in 1 way.
4057 is the sum of 2 positive triangular numbers.
4057 is the difference of 2 positive pentagonal numbers in 1 way.
4057 = 242 + 592 is the sum of 2 positive squares in 1 way.
4057 = 42 + 212 + 602 is the sum of 3 positive squares.
40572 = 28322 + 29052 is the sum of 2 positive squares in 1 way.
40572 is the sum of 3 positive squares.
4057 is a proper divisor of 14096 - 1.
4057 is an emirp in (at least) the following bases: 4, 7, 9, 13, 15, 19, 23, 24, 28, 34, 43, 45, 49, 50, 51, 57, 59, 61, 63, 64, 67, 68, 69, 73, 77, 81, 87, 89, 93, 94, 98, and 99.
4057 is palindromic in (at least) the following bases: 52, -12, -22, -25, and -78.
4057 in base 5 = 112212 and consists of only the digits '1' and '2'.
4057 in base 21 = 944 and consists of only the digits '4' and '9'.
4057 in base 22 = 889 and consists of only the digits '8' and '9'.
4057 in base 24 = 711 and consists of only the digits '1' and '7'.
4057 in base 51 = 1SS and consists of only the digits '1' and 'S'.
4057 in base 52 = 1Q1 and consists of only the digits '1' and 'Q'.

The number 4057 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A025019: Smallest prime in Goldbach partition of A025018(n).
A031934: Lower prime of a pair of consecutive primes having a difference of 16.
A045710: Primes with first digit 4.
A059245: Primes p such that x^13 = 2 has no solution mod p.
A098182: a(n) = 3*a(n-1) - a(n-2) + a(n-3), a(0)=1,a(1)=1,a(2)=3.
A104803: "Floor of hypotenuses": a(n) = floor(sqrt(a(n-1)^2 + a(n-2)^2)), a(1)=1, a(2)=3.
A136065: Mother primes of order 6.
A200838: T(n,k)=Number of 0..k arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases
A212729: T(n,k)=Number of 0..2 arrays of length n+2*k-1 with sum less than 2*k in any length 2k subsequence (=less than 50% duty cycle)
A216451: Numbers which are simultaneously of the form x^2+y^2, x^2+2y^2, x^2+3y^2, x^2+7y^2, all with x>0, y>0.

Tuesday, September 12, 2017

Number of the day: 5382

Properties of the number 5382:

5382 = 2 × 32 × 13 × 23 is the 4672th composite number and is not squarefree.
5382 has 4 distinct prime factors, 24 divisors, 15 antidivisors and 1584 totatives.
5382 has an oblong digit product 240 in base 10.
5382 = 142 + … + 262 is the sum of at least 2 consecutive positive squares in 1 way.
5382 is the sum of 2 positive triangular numbers.
5382 is the difference of 2 positive pentagonal numbers in 2 ways.
5382 = 22 + 72 + 732 is the sum of 3 positive squares.
53822 = 20702 + 49682 is the sum of 2 positive squares in 1 way.
53822 is the sum of 3 positive squares.
5382 is a proper divisor of 1393 - 1.
5382 is palindromic in (at least) the following bases: 28, 77, -4, and -32.
5382 in base 17 = 11aa and consists of only the digits '1' and 'a'.
5382 in base 28 = 6o6 and consists of only the digits '6' and 'o'.

The number 5382 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A055102: Expansion of cube of continued fraction 1/ ( 1+q/ ( 1+q^2/ ( 1+q^3/ ( 1+q^4/... )))).
A077285: Number of partitions of n with designated summands.
A086113: Number of 3 X n (0,1) matrices such that each row and each column is nondecreasing or nonincreasing.
A113744: Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 7 multiples of n-1, n-2, ..., 1, for n>=1.
A113746: Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 9 multiples of n-1, n-2, ..., 1, for n>=1.
A134602: Composite numbers such that the square mean of their prime factors is a nonprime integer (where the prime factors are taken with multiplicity and the square mean of c and d is sqrt((c^2+d^2)/2)).
A139274: a(n) = n*(8*n-1).
A152759: 3 times 9-gonal (or nonagonal) numbers: 3n(7n-5)/2.
A182205: Iterate the map in A006368 starting at 40.
A186029: a(n) = n*(7*n+3)/2.

Monday, September 11, 2017

Number of the day: 573272362

Properties of the number 573272362:

573272362 = 2 × 13 × 1559 × 14143 is the 543271742th composite number and is squarefree.
573272362 has 4 distinct prime factors, 16 divisors, 53 antidivisors and 264398832 totatives.
573272362 has an emirp digit sum 37 in base 10.
573272362 is the difference of 2 positive pentagonal numbers in 5 ways.
573272362 = 482 + 532 + 239432 is the sum of 3 positive squares.
5732723622 = 2204893702 + 5291744882 is the sum of 2 positive squares in 1 way.
5732723622 is the sum of 3 positive squares.
573272362 is a proper divisor of 124996637 - 1.
573272362 = '57' + '3272362' is the concatenation of 2 semiprime numbers.

Sunday, September 10, 2017

Number of the day: 239515396887

Properties of the number 239515396887:

239515396887 = 3 × 13 × 43 × 142823731 is composite and squarefree.
239515396887 has 4 distinct prime factors, 16 divisors, 25 antidivisors and 143966319840 totatives.
239515396887 has a sphenic digit sum 66 in base 10.
239515396887 has a triangular digit sum 66 in base 10.
239515396887 = 1197576984442 - 1197576984432 = 399192328162 - 399192328132 = 92121306562 - 92121306432 = 30707102362 - 30707101972 = 27850627762 - 27850627332 = 9283543162 - 9283541872 = 2142358762 - 2142353172 = 714127042 - 714110272 is the difference of 2 nonnegative squares in 8 ways.
239515396887 is the difference of 2 positive pentagonal numbers in 4 ways.
239515396887 is not the sum of 3 positive squares.
2395153968872 = 921213064952 + 2210911355882 is the sum of 2 positive squares in 1 way.
2395153968872 is the sum of 3 positive squares.
239515396887 is a proper divisor of 10972720452 - 1.
239515396887 = '239' + '515396887' is the concatenation of 2 prime numbers.
239515396887 = '23951' + '5396887' is the concatenation of 2 semiprime numbers.

Saturday, September 9, 2017

Number of the day: 2758

Properties of the number 2758:

2758 = 2 × 7 × 197 is a sphenic number and squarefree.
2758 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 1176 totatives.
2758 has a semiprime digit sum 22 in base 10.
2758 is the difference of 2 positive pentagonal numbers in 4 ways.
2758 = 62 + 112 + 512 is the sum of 3 positive squares.
27582 = 3922 + 27302 is the sum of 2 positive squares in 1 way.
27582 is the sum of 3 positive squares.
2758 is a proper divisor of 2114 - 1.
2758 is palindromic in (at least) the following bases: 29, -15, -21, -27, and -52.
2758 in base 14 = 1010 and consists of only the digits '0' and '1'.
2758 in base 17 = 994 and consists of only the digits '4' and '9'.
2758 in base 26 = 422 and consists of only the digits '2' and '4'.
2758 in base 28 = 3ee and consists of only the digits '3' and 'e'.
2758 in base 29 = 383 and consists of only the digits '3' and '8'.
2758 in base 52 = 112 and consists of only the digits '1' and '2'.

The number 2758 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A022265: a(n) = n*(7*n + 1)/2.
A034262: a(n) = n^3 + n.
A052284: Number of compositions of n into nonprime numbers.
A177915: Numbers n such that n^3 divides 15^(n^2)-1.
A182714: Number of 4's in the last section of the set of partitions of n.
A200809: T(n,k)=Number of nXk 0..2 arrays with no average of any element and its diagonal, antidiagonal, horizontal and vertical neighbors equal to one
A227631: Array t(n,k): row n consists of the positive integers m for which the least splitter of H(m) and H(m+1) is n, where H denotes harmonic number.
A229308: Primitive numbers in A229304.
A229309: Primitive numbers in A229305.
A261380: T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with each 3X3 subblock having clockwise perimeter pattern 00001011 00010101 or 01010101.

Friday, September 8, 2017

Number of the day: 853002

Marin Mersenne was born on this day 429 years ago.

Properties of the number 853002:

853002 = 2 × 32 × 47389 is the 785163th composite number and is not squarefree.
853002 has 3 distinct prime factors, 12 divisors, 21 antidivisors and 284328 totatives.
853002 is the sum of 2 positive triangular numbers.
853002 = 692 + 9212 is the sum of 2 positive squares in 1 way.
853002 = 522 + 972 + 9172 is the sum of 3 positive squares.
8530022 = 1270982 + 8434802 is the sum of 2 positive squares in 1 way.
8530022 is the sum of 3 positive squares.
853002 is a proper divisor of 80922 - 1.