Thursday, June 30, 2016

Number of the day: 9562

Properties of the number 9562:

9562 = 2 × 7 × 683 is a sphenic number and squarefree.
9562 has 3 distinct prime factors, 8 divisors, 27 antidivisors and 4092 totatives.
9562 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 9562 results in a prime.
9562 is the difference of 2 positive pentagonal numbers in 4 ways.
9562 = 122 + 432 + 872 is the sum of 3 positive squares.
95622 is the sum of 3 positive squares.
9562 is a divisor of 13673 - 1.
9562 = '9' + '562' is the concatenation of 2 semiprime numbers.
9562 is palindromic in (at least) the following bases: 34, 35, -39, and -54.
9562 in base 3 = 111010011 and consists of only the digits '0' and '1'.
9562 in base 4 = 2111122 and consists of only the digits '1' and '2'.
9562 in base 13 = 4477 and consists of only the digits '4' and '7'.
9562 in base 33 = 8pp and consists of only the digits '8' and 'p'.
9562 in base 34 = 898 and consists of only the digits '8' and '9'.
9562 in base 35 = 7s7 and consists of only the digits '7' and 's'.

The number 9562 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A025002: a(1) = 7; a(n+1) = a(n)-th nonprime, where nonprimes begin at 0.
A043579: Numbers n such that base 2 representation has exactly 12 runs.
A045108: Numbers n with property that in base 4 representation the numbers of 1's and 2's are 4 and 3, respectively.
A101535: Indices of primes in sequence defined by A(0) = 63, A(n) = 10*A(n-1) + 43 for n > 0.
A136170: Triangle T, read by rows, where row n of T = row n-1 of T^fibonacci(n) with appended '1' for n>=1 starting with a single '1' in row 0.
A164387: Number of binary strings of length n with no substrings equal to 0000 or 0010
A172113: Partial sums of the generalized Cuban primes A007645.
A184035: 1/16 the number of (n+1)X6 0..3 arrays with all 2X2 subblocks having the same four values
A241563: Number of 3-element subsets of {1,...,n} whose sum has more than 2 divisors.
A263466: Least k such that prime(n) is the smallest prime p for which k^2 + p^2 is also prime, or 0 if none.

Wednesday, June 29, 2016

Number of the day: 148782

Properties of the number 148782:

148782 = 2 × 3 × 137 × 181 is the 135044th composite number and is squarefree.
148782 has 4 distinct prime factors, 16 divisors, 11 antidivisors and 48960 totatives.
148782 has a sphenic digit sum 30 in base 10.
148782 has an oblong digit sum 30 in base 10.
Reversing the decimal digits of 148782 results in a semiprime.
148782 is the sum of 2 positive triangular numbers.
148782 is the difference of 2 positive pentagonal numbers in 2 ways.
148782 = 142 + 192 + 3852 is the sum of 3 positive squares.
1487822 = 955682 + 1140302 = 830702 + 1234322 = 1033682 + 1070102 = 156182 + 1479602 is the sum of 2 positive squares in 4 ways.
1487822 is the sum of 3 positive squares.
148782 is a divisor of 85920 - 1.
148782 = '14' + '8782' is the concatenation of 2 semiprime numbers.
148782 is palindromic in (at least) the following bases: -59, -60, and -92.
148782 in base 57 = jjC and consists of only the digits 'C' and 'j'.
148782 in base 59 = ghh and consists of only the digits 'g' and 'h'.

Tuesday, June 28, 2016

Number of the day: 6282016

Henri Léon Lebesgue was born on this day 141 years ago.

Happy τ Day!

Properties of the number 6282016:

6282016 = 25 × 13 × 15101 is the 5851121th composite number and is not squarefree.
6282016 has 3 distinct prime factors, 24 divisors, 7 antidivisors and 2899200 totatives.
6282016 has a semiprime digit sum 25 in base 10.
Reversing the decimal digits of 6282016 results in a sphenic number.
6282016 = 15705052 - 15705032 = 7852542 - 7852502 = 3926302 - 3926222 = 1963212 - 1963052 = 1208212 - 1207952 = 604302 - 603782 = 302542 - 301502 = 152052 - 149972 is the difference of 2 nonnegative squares in 8 ways.
6282016 is the sum of 2 positive triangular numbers.
6282016 is the difference of 2 positive pentagonal numbers in 4 ways.
6282016 = 17402 + 18042 = 9962 + 23002 is the sum of 2 positive squares in 2 ways.
6282016 = 42 + 4802 + 24602 is the sum of 3 positive squares.
62820162 = 24161602 + 57987842 = 2268162 + 62779202 = 42979842 + 45816002 = 22052162 + 58822402 is the sum of 2 positive squares in 4 ways.
62820162 is the sum of 3 positive squares.
6282016 is a divisor of 83960 - 1.

Monday, June 27, 2016

Number of the day: 360534489

Properties of the number 360534489:

360534489 = 3 × 7 × 43 × 399263 is the 341196353th composite number and is squarefree.
360534489 has 4 distinct prime factors, 16 divisors, 17 antidivisors and 201228048 totatives.
360534489 has a sphenic digit sum 42 in base 10.
360534489 has an oblong digit sum 42 in base 10.
Reversing the decimal digits of 360534489 results in a semiprime.
360534489 = 1802672452 - 1802672442 = 600890832 - 600890802 = 257524672 - 257524602 = 85841652 - 85841442 = 41922832 - 41922402 = 13974852 - 13973562 = 5990452 - 5987442 = 2000832 - 1991802 is the difference of 2 nonnegative squares in 8 ways.
360534489 is the sum of 2 positive triangular numbers.
360534489 is the difference of 2 positive pentagonal numbers in 4 ways.
360534489 = 1372 + 2182 + 189862 is the sum of 3 positive squares.
3605344892 is the sum of 3 positive squares.
360534489 is a divisor of 154935229 - 1.
360534489 = '36053' + '4489' is the concatenation of 2 semiprime numbers.
360534489 = '3605' + '34489' is the concatenation of 2 sphenic numbers.

Sunday, June 26, 2016

Number of the day: 773031

Properties of the number 773031:

773031 = 3 × 7 × 131 × 281 is the 711071th composite number and is squarefree.
773031 has 4 distinct prime factors, 16 divisors, 23 antidivisors and 436800 totatives.
773031 has a semiprime digit sum 21 in base 10.
773031 has a Fibonacci digit sum 21 in base 10.
773031 has a triangular digit sum 21 in base 10.
Reversing the decimal digits of 773031 results in a sphenic number.
773031 = 3865162 - 3865152 = 1288402 - 1288372 = 552202 - 552132 = 184162 - 183952 = 30162 - 28852 = 15162 - 12352 = 11802 - 7872 = 8802 - 372 is the difference of 2 nonnegative squares in 8 ways.
773031 is the sum of 2 positive triangular numbers.
773031 is the difference of 2 positive pentagonal numbers in 2 ways.
773031 is not the sum of 3 positive squares.
7730312 = 4401602 + 6354812 is the sum of 2 positive squares in 1 way.
7730312 is the sum of 3 positive squares.
773031 is a divisor of 5360 - 1.
773031 = '77' + '3031' is the concatenation of 2 semiprime numbers.

Saturday, June 25, 2016

Number of the day: 21368

Properties of the number 21368:

21368 = 23 × 2671 is the 18970th composite number and is not squarefree.
21368 has 2 distinct prime factors, 8 divisors, 31 antidivisors and 10680 totatives.
21368 has an oblong digit sum 20 in base 10.
21368 = 53432 - 53412 = 26732 - 26692 is the difference of 2 nonnegative squares in 2 ways.
21368 is the sum of 2 positive triangular numbers.
21368 = 42 + 62 + 1462 is the sum of 3 positive squares.
213682 is the sum of 3 positive squares.
21368 is a divisor of 3730 - 1.
21368 is palindromic in (at least) base -35.
21368 in base 13 = 9959 and consists of only the digits '5' and '9'.
21368 in base 34 = igg and consists of only the digits 'g' and 'i'.

The number 21368 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006601: Numbers n such that n, n+1, n+2 and n+3 have the same number of divisors.
A102186: The PDO(n) function (Partitions with Designated summands in which all parts are Odd): the sum of products of multiplicities of parts in all partitions of n into odd parts.
A108433: Triangle read by rows: T(n,k) is number of paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(2,1), U=(1,2), or d=(1,-1) and have k hills of the form ud (a hill is either a ud or a Udd starting at the x-axis).
A124401: Indices where 2 occurs in A124151.
A127936: Numbers n such that 1 + Sum_{i=1..n} 2^(2i-1) is prime.
A180249: a(n) is the total number of k-reverses of n.
A220031: Number of nX7 arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..1 nX7 array
A238491: Number of partitions of n not containing 3*(number of parts) as a part.

Friday, June 24, 2016

Number of the day: 8444273062

Properties of the number 8444273062:

8444273062 = 2 × 4222136531 is semiprime and squarefree.
8444273062 has 2 distinct prime factors, 4 divisors, 47 antidivisors and 4222136530 totatives.
8444273062 is the sum of 2 positive triangular numbers.
8444273062 is the difference of 2 positive pentagonal numbers in 2 ways.
8444273062 = 8662 + 38252 + 918092 is the sum of 3 positive squares.
84442730622 is the sum of 3 positive squares.
8444273062 is a divisor of 19422213653 - 1.
8444273062 is an emirpimes in (at least) the following bases: 2, 14, 17, 23, 25, 26, 28, 30, 34, 44, 46, 50, 53, 56, 65, 74, 86, 96, and 98.

Thursday, June 23, 2016

Number of the day: 95385

Alan Turing was born on this day 104 years ago.

Properties of the number 95385:

95385 = 3 × 5 × 6359 is a sphenic number and squarefree.
95385 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 50864 totatives.
95385 has a sphenic digit sum 30 in base 10.
95385 has an oblong digit sum 30 in base 10.
95385 = 476932 - 476922 = 158992 - 158962 = 95412 - 95362 = 31872 - 31722 is the difference of 2 nonnegative squares in 4 ways.
95385 is the sum of 2 positive triangular numbers.
95385 is the difference of 2 positive pentagonal numbers in 2 ways.
95385 = 112 + 202 + 3082 is the sum of 3 positive squares.
953852 = 572312 + 763082 is the sum of 2 positive squares in 1 way.
953852 is the sum of 3 positive squares.
95385 is a divisor of 109122 - 1.

Wednesday, June 22, 2016

Number of the day: 603372173282

Hermann Minkowski was born on this day 152 years ago.

Properties of the number 603372173282:

603372173282 = 2 × 1889 × 159706769 is a sphenic number and squarefree.
603372173282 has 3 distinct prime factors, 8 divisors, 39 antidivisors and 301526377984 totatives.
Reversing the decimal digits of 603372173282 results in a semiprime.
603372173282 is the difference of 2 positive pentagonal numbers in 2 ways.
603372173282 = 3365812 + 7000612 = 2704212 + 7281792 is the sum of 2 positive squares in 2 ways.
603372173282 = 50792 + 53962 + 7767352 is the sum of 3 positive squares.
6033721732822 = 4187511483182 + 4344024116802 = 3767986341602 + 4712544628822 = 3938297867182 + 4571171388002 = 557800203182 + 6007882895202 is the sum of 2 positive squares in 4 ways.
6033721732822 is the sum of 3 positive squares.
603372173282 is a divisor of 33112285136 - 1.

Tuesday, June 21, 2016

Number of the day: 77204377

Properties of the number 77204377:

77204377 = 271 × 347 × 821 is a sphenic number and squarefree.
77204377 has 3 distinct prime factors, 8 divisors, 23 antidivisors and 76604400 totatives.
77204377 has an emirp digit sum 37 in base 10.
77204377 = 386021892 - 386021882 = 1425792 - 1423082 = 1114192 - 1110722 = 474292 - 466082 is the difference of 2 nonnegative squares in 4 ways.
77204377 is the difference of 2 positive pentagonal numbers in 4 ways.
77204377 = 1522 + 4832 + 87722 is the sum of 3 positive squares.
772043772 = 403418732 + 658259002 is the sum of 2 positive squares in 1 way.
772043772 is the sum of 3 positive squares.
77204377 is a divisor of 68315570 - 1.
77204377 = '772043' + '77' is the concatenation of 2 semiprime numbers.

Monday, June 20, 2016

Number of the day: 462403898167

Properties of the number 462403898167:

462403898167 = 2753 × 167963639 is semiprime and squarefree.
462403898167 has 2 distinct prime factors, 4 divisors, 67 antidivisors and 462235931776 totatives.
462403898167 has an emirpimes digit sum 58 in base 10.
462403898167 = 2312019490842 - 2312019490832 = 839831962 - 839804432 is the difference of 2 nonnegative squares in 2 ways.
462403898167 is the sum of 2 positive triangular numbers.
462403898167 is the difference of 2 positive pentagonal numbers in 2 ways.
462403898167 is not the sum of 3 positive squares.
4624038981672 = 1222775291922 + 4459434615452 is the sum of 2 positive squares in 1 way.
4624038981672 is the sum of 3 positive squares.
462403898167 is a divisor of 617182846492 - 1.
462403898167 = '462403' + '898167' is the concatenation of 2 semiprime numbers.
462403898167 is an emirpimes in (at least) the following bases: 3, 4, 6, 13, 17, 20, 27, 29, 31, 32, 33, 41, 42, 43, 45, 49, 50, 51, 52, 53, 59, 66, 70, 71, 73, 74, 79, 80, 81, 86, 88, 89, 94, 97, 98, and 100.

Sunday, June 19, 2016

Number of the day: 38680245334015

Blaise Pascal was born on this day 393 years ago.

Properties of the number 38680245334015:

38680245334015 = 5 × 89 × 18553 × 4685059 is composite and squarefree.
38680245334015 has 4 distinct prime factors, 16 divisors, 23 antidivisors and 30594852997632 totatives.
Reversing the decimal digits of 38680245334015 results in a sphenic number.
38680245334015 = 193401226670082 - 193401226670072 = 38680245334042 - 38680245333992 = 2173047491122 - 2173047490232 = 434609500362 - 434609495912 = 10424349042 - 10424163512 = 2085315082 - 2084387432 = 125382562 - 108870392 = 64705722 - 17855132 is the difference of 2 nonnegative squares in 8 ways.
38680245334015 is the difference of 2 positive pentagonal numbers in 8 ways.
38680245334015 is not the sum of 3 positive squares.
386802453340152 = 169497704272652 + 347687598508002 = 74303161716402 + 379598706621752 = 253272415516402 + 292351195394252 = 73014395686682 + 379848701369992 = 27207215176572 + 385844405625242 = 168316694599932 + 348260862327242 = 176451456242812 + 344210722522922 = 81917507005562 + 378028649649672 = 259097068267562 + 287201753346172 = 232081472004092 + 309441962672122 = 144621961856842 + 358748694852872 = 239286717941372 + 303904597738842 = 99551647426252 + 373772132996402 is the sum of 2 positive squares in 13 ways.
386802453340152 is the sum of 3 positive squares.
38680245334015 is a divisor of 31221009976 - 1.

Saturday, June 18, 2016

Number of the day: 45167

Properties of the number 45167:

45167 = 312 × 47 is the 40478th composite number and is not squarefree.
45167 has 2 distinct prime factors, 6 divisors, 23 antidivisors and 42780 totatives.
45167 has a prime digit sum 23 in base 10.
45167 = 225842 - 225832 = 7442 - 7132 = 5042 - 4572 is the difference of 2 nonnegative squares in 3 ways.
45167 is the difference of 2 positive pentagonal numbers in 3 ways.
45167 is not the sum of 3 positive squares.
451672 is the sum of 3 positive squares.
45167 is a divisor of 169315 - 1.
45167 is palindromic in (at least) the following bases: 41, and 44.
45167 in base 41 = QZQ and consists of only the digits 'Q' and 'Z'.
45167 in base 42 = PPH and consists of only the digits 'H' and 'P'.
45167 in base 44 = NEN and consists of only the digits 'E' and 'N'.

The number 45167 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A015247: (2n-15)n^2.
A036659: Product of n with sum of next n consecutive integers.
A064977: n*10^3-1, n*10^3-3, n*10^3-7 and n*10^3-9 are all prime.
A266771: Molien series for invariants of finite Coxeter group D_8 (bisected).

Friday, June 17, 2016

Number of the day: 86315

Properties of the number 86315:

86315 = 5 × 61 × 283 is a sphenic number and squarefree.
86315 has 3 distinct prime factors, 8 divisors, 13 antidivisors and 67680 totatives.
86315 has a prime digit sum 23 in base 10.
86315 = 431582 - 431572 = 86342 - 86292 = 7382 - 6772 = 2942 - 112 is the difference of 2 nonnegative squares in 4 ways.
86315 is the difference of 2 positive pentagonal numbers in 3 ways.
86315 = 52 + 212 + 2932 is the sum of 3 positive squares.
863152 = 517892 + 690522 = 384882 + 772592 = 585812 + 633922 = 155652 + 849002 is the sum of 2 positive squares in 4 ways.
863152 is the sum of 3 positive squares.
86315 is a divisor of 16974 - 1.
86315 is palindromic in (at least) the following bases: 67, 87, and -53.
86315 in base 20 = afff and consists of only the digits 'a' and 'f'.
86315 in base 52 = Vll and consists of only the digits 'V' and 'l'.

The number 86315 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A262016: a(n) = ( ( Sum_{k=1..n} 2^(prime(k)-1) ) mod n! ) / 2.

Thursday, June 16, 2016

Number of the day: 312408369436380

Properties of the number 312408369436380:

312408369436380 = 22 × 3 × 5 × 7 × 743829451039 is composite and not squarefree.
312408369436380 has 5 distinct prime factors, 48 divisors, 47 antidivisors and 71407627299648 totatives.
312408369436380 = 781020923590962 - 781020923590942 = 260340307863682 - 260340307863622 = 156204184718242 - 156204184718142 = 111574417655922 - 111574417655782 = 52068061572882 - 52068061572582 = 37191472552162 - 37191472551742 = 22314883531522 - 22314883530822 = 7438294511442 - 7438294509342 is the difference of 2 nonnegative squares in 8 ways.
312408369436380 is the difference of 2 positive pentagonal numbers in 4 ways.
312408369436380 is not the sum of 3 positive squares.
3124083694363802 = 1874450216618282 + 2499266955491042 is the sum of 2 positive squares in 1 way.
3124083694363802 is the sum of 3 positive squares.
312408369436380 is a divisor of 23982647716782 - 1.

Wednesday, June 15, 2016

Number of the day: 41088

Properties of the number 41088:

41088 = 27 × 3 × 107 is the 36787th composite number and is not squarefree.
41088 has 3 distinct prime factors, 32 divisors, 15 antidivisors and 13568 totatives.
41088 has a semiprime digit sum 21 in base 10.
41088 has a Fibonacci digit sum 21 in base 10.
41088 has a triangular digit sum 21 in base 10.
Reversing the decimal digits of 41088 results in a sphenic number.
41088 is the difference of 2 nonnegative squares in 12 ways.
41088 is the difference of 2 positive pentagonal numbers in 1 way.
41088 = 82 + 322 + 2002 is the sum of 3 positive squares.
410882 is the sum of 3 positive squares.
41088 is a divisor of 6412 - 1.
41088 is palindromic in (at least) the following bases: 35, 82, and -43.
41088 in base 4 = 22002000 and consists of only the digits '0' and '2'.
41088 in base 35 = xix and consists of only the digits 'i' and 'x'.
41088 in base 42 = NCC and consists of only the digits 'C' and 'N'.
41088 in base 46 = JJA and consists of only the digits 'A' and 'J'.
41088 in base 58 = CCO and consists of only the digits 'C' and 'O'.

The number 41088 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A202048: Number of (n+2)X6 binary arrays avoiding patterns 001 and 110 in rows and columns
A202050: Number of (n+2)X8 binary arrays avoiding patterns 001 and 110 in rows and columns
A202052: T(n,k)=Number of (n+2)X(k+2) binary arrays avoiding patterns 001 and 110 in rows and columns
A217202: Triangle read by rows, arising in enumeration of permutations by cyclic valleys, cycles and fixed points.
A217205: Triangle read by rows, related to Bell numbers A000110.
A252726: Number of (7+2)X(n+2) 0..3 arrays with every consecutive three elements in every row and diagonal having exactly two distinct values, and in every column and antidiagonal not having exactly two distinct values, and new values 0 upwards introduced in row major order

Tuesday, June 14, 2016

Number of the day: 451630

Andrey Andreyevich Markov was born on this day 160 years ago.

Properties of the number 451630:

451630 = 2 × 5 × 19 × 2377 is the 413789th composite number and is squarefree.
451630 has 4 distinct prime factors, 16 divisors, 23 antidivisors and 171072 totatives.
451630 has a prime digit sum 19 in base 10.
451630 is the difference of 2 positive pentagonal numbers in 4 ways.
451630 = 352 + 2822 + 6092 is the sum of 3 positive squares.
4516302 = 2840502 + 3511202 = 165682 + 4513262 = 1104662 + 4379122 = 2709782 + 3613042 is the sum of 2 positive squares in 4 ways.
4516302 is the sum of 3 positive squares.
451630 is a divisor of 120118 - 1.
451630 is palindromic in (at least) base 37.
451630 in base 37 = 8XX8 and consists of only the digits '8' and 'X'.

Monday, June 13, 2016

Number of the day: 59816789749690

John Forbes Nash, Jr. was born on this day 88 years ago.

Properties of the number 59816789749690:

59816789749690 = 2 × 5 × 4951 × 1208175919 is composite and squarefree.
59816789749690 has 4 distinct prime factors, 16 divisors, 27 antidivisors and 23921883176400 totatives.
59816789749690 is the difference of 2 positive pentagonal numbers in 4 ways.
59816789749690 = 132602 + 204792 + 77340932 is the sum of 3 positive squares.
598167897496902 = 358900738498142 + 478534317997522 is the sum of 2 positive squares in 1 way.
598167897496902 is the sum of 3 positive squares.
59816789749690 is a divisor of 315034066325 - 1.

Sunday, June 12, 2016

Number of the day: 5286185

Vladimir Igorevich Arnold was born on this day 79 years ago.

Properties of the number 5286185:

5286185 = 5 × 1057237 is semiprime and squarefree.
5286185 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 4228944 totatives.
5286185 has a semiprime digit sum 35 in base 10.
5286185 = 26430932 - 26430922 = 5286212 - 5286162 is the difference of 2 nonnegative squares in 2 ways.
5286185 is the difference of 2 positive pentagonal numbers in 2 ways.
5286185 = 13572 + 18562 = 282 + 22992 is the sum of 2 positive squares in 2 ways.
5286185 = 342 + 652 + 22982 is the sum of 3 positive squares.
52861852 = 31717112 + 42289482 = 1287442 + 52846172 = 16032872 + 50371842 = 30677752 + 43049402 is the sum of 2 positive squares in 4 ways.
52861852 is the sum of 3 positive squares.
5286185 is a divisor of 13219274 - 1.
5286185 is an emirpimes in (at least) the following bases: 7, 13, 16, 17, 18, 22, 23, 25, 31, 32, 45, 46, 47, 48, 57, 61, 65, 69, 73, 75, 78, 88, 89, 90, 97, 99, and 100.
5286185 is palindromic in (at least) base -28.

Saturday, June 11, 2016

Number of the day: 870874186315877

Properties of the number 870874186315877:

870874186315877 is prime.
870874186315877 has 21 antidivisors and 870874186315876 totatives.
870874186315877 = 4354370931579392 - 4354370931579382 is the difference of 2 nonnegative squares in 1 way.
870874186315877 is the difference of 2 positive pentagonal numbers in 1 way.
870874186315877 = 195315862 + 221221912 is the sum of 2 positive squares in 1 way.
870874186315877 = 78472 + 162782 + 295105722 is the sum of 3 positive squares.
8708741863158772 = 1079084829650852 + 8641629520498522 is the sum of 2 positive squares in 1 way.
8708741863158772 is the sum of 3 positive squares.
870874186315877 is a divisor of 1079466023764303 - 1.
870874186315877 = '870874' + '186315877' is the concatenation of 2 semiprime numbers.
870874186315877 is an emirp in (at least) the following bases: 13, 67, 84, 86, 88, and 95.

Friday, June 10, 2016

Number of the day: 58430163

Properties of the number 58430163:

58430163 = 3 × 11 × 43 × 41177 is the 54955741th composite number and is squarefree.
58430163 has 4 distinct prime factors, 16 divisors, 25 antidivisors and 34587840 totatives.
58430163 has a sphenic digit sum 30 in base 10.
58430163 has an oblong digit sum 30 in base 10.
58430163 = 292150822 - 292150812 = 97383622 - 97383592 = 26559222 - 26559112 = 8853222 - 8852892 = 6794422 - 6793992 = 2265382 - 2264092 = 620022 - 615292 = 212982 - 198792 is the difference of 2 nonnegative squares in 8 ways.
58430163 is the difference of 2 positive pentagonal numbers in 4 ways.
58430163 = 1552 + 2872 + 76372 is the sum of 3 positive squares.
584301632 = 294797252 + 504482882 is the sum of 2 positive squares in 1 way.
584301632 is the sum of 3 positive squares.
58430163 is a divisor of 85920588 - 1.
58430163 = '58' + '430163' is the concatenation of 2 semiprime numbers.

Thursday, June 9, 2016

Number of the day: 538370

John Edensor Littlewood was born on this day 131 years ago.

Properties of the number 538370:

538370 = 2 × 5 × 7 × 7691 is the 493915th composite number and is squarefree.
538370 has 4 distinct prime factors, 16 divisors, 19 antidivisors and 184560 totatives.
538370 has an emirpimes digit sum 26 in base 10.
538370 = 1502 + … + 1702 is the sum of at least 2 consecutive positive squares in 1 way.
538370 is the difference of 2 positive pentagonal numbers in 4 ways.
538370 = 42 + 1252 + 7232 is the sum of 3 positive squares.
5383702 = 3230222 + 4306962 is the sum of 2 positive squares in 1 way.
5383702 is the sum of 3 positive squares.
538370 is a divisor of 140930 - 1.
538370 is palindromic in (at least) the following bases: 98, and -8.

Wednesday, June 8, 2016

Number of the day: 9073

Properties of the number 9073:

9073 = 43 × 211 is semiprime and squarefree.
9073 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 8820 totatives.
9073 has a prime digit sum 19 in base 10.
Reversing the decimal digits of 9073 results in a prime.
9073 = 45372 - 45362 = 1272 - 842 is the difference of 2 nonnegative squares in 2 ways.
9073 is the sum of 2 positive triangular numbers.
9073 is the difference of 2 positive pentagonal numbers in 2 ways.
9073 = 92 + 442 + 842 is the sum of 3 positive squares.
90732 is the sum of 3 positive squares.
9073 is a divisor of 8596 - 1.
9073 = '907' + '3' is the concatenation of 2 prime numbers.
9073 is an emirpimes in (at least) the following bases: 6, 7, 9, 11, 12, 14, 16, 18, 20, 21, 23, 25, 26, 28, 33, 35, 39, 41, 42, 43, 46, 48, 49, 55, 56, 57, 59, 61, 63, 64, 67, 69, 73, 77, 78, 79, 80, 85, 86, 88, 90, 92, 93, 94, 96, and 97.
9073 is palindromic in (at least) the following bases: 72, 81, 84, and -35.
9073 in base 3 = 110110001 and consists of only the digits '0' and '1'.
9073 in base 6 = 110001 and consists of only the digits '0' and '1'.
9073 in base 27 = cc1 and consists of only the digits '1' and 'c'.

The number 9073 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A020142: Pseudoprimes to base 14.
A020159: Pseudoprimes to base 31.
A064910: Smallest semiprime p1*p2 such that p2 mod p1 = n.
A069190: Centered 24-gonal numbers.
A074341: a(1) = 4; a(n) is smallest number > a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.
A078293: Least nontrivial multiple of the n-th prime beginning with 9.
A113690: Semiprimes in A054552.
A118589: E.g.f.: A(x) = exp(x + x^2 + x^3).
A199744: G.f.: 1/(1+x+2*x^2+2*x^3+x^4).
A261764: Triangle read by rows: T(n,k) is the number of nilpotent subpermutations on an n-set, each of nilpotency index less than or equal to k.

Tuesday, June 7, 2016

Number of the day: 593113553

Properties of the number 593113553:

593113553 = 61 × 1181 × 8233 is a sphenic number and squarefree.
593113553 has 3 distinct prime factors, 8 divisors, 83 antidivisors and 582825600 totatives.
593113553 has a semiprime digit sum 35 in base 10.
Reversing the decimal digits of 593113553 results in a semiprime.
593113553 = 2965567772 - 2965567762 = 48616172 - 48615562 = 2516972 - 2505162 = 401372 - 319042 is the difference of 2 nonnegative squares in 4 ways.
593113553 is the difference of 2 positive pentagonal numbers in 4 ways.
593113553 = 109132 + 217722 = 41832 + 239922 = 68082 + 233832 = 2122 + 243532 is the sum of 2 positive squares in 4 ways.
593113553 = 142 + 6212 + 243462 is the sum of 3 positive squares.
5931135532 = 4034024552 + 4347989722 = 2611486252 + 5325270722 = 967822952 + 5851639722 = 3183829282 + 5004158252 = 1608380282 + 5708894952 = 103256722 + 5930236652 = 3549264152 + 4751956722 = 3528969722 + 4767047452 = 2007170722 + 5581185752 = 2703799532 + 5278999602 = 1069549032 + 5833903802 = 655264472 + 5894828002 = 1707524202 + 5680029032 is the sum of 2 positive squares in 13 ways.
5931135532 is the sum of 3 positive squares.
593113553 is a divisor of 3980 - 1.
593113553 = '59311' + '3553' is the concatenation of 2 sphenic numbers.
593113553 in base 60 = jjrjr and consists of only the digits 'j' and 'r'.

Monday, June 6, 2016

Number of the day: 729082

Aleksandr Mikhailovich Lyapunov was born on this day 159 years ago.

Properties of the number 729082:

729082 = 2 × 364541 is semiprime and squarefree.
729082 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 364540 totatives.
729082 has a triangular digit sum 28 in base 10.
Reversing the decimal digits of 729082 results in a prime.
729082 is the difference of 2 positive pentagonal numbers in 2 ways.
729082 = 912 + 8492 is the sum of 2 positive squares in 1 way.
729082 = 482 + 1272 + 8432 is the sum of 3 positive squares.
7290822 = 1545182 + 7125202 is the sum of 2 positive squares in 1 way.
7290822 is the sum of 3 positive squares.
729082 is a divisor of 2276628 - 1.
729082 is an emirpimes in (at least) the following bases: 2, 8, 12, 14, 15, 16, 17, 34, 35, 36, 41, 42, 58, 61, 63, 68, 71, 74, 78, 82, 84, 86, 90, 92, and 96.
729082 in base 3 = 1101001010001 and consists of only the digits '0' and '1'.

Sunday, June 5, 2016

Number of the day: 8604792

Properties of the number 8604792:

8604792 = 23 × 34 × 72 × 271 is the 8027044th composite number and is not squarefree.
8604792 has 4 distinct prime factors, 120 divisors, 35 antidivisors and 2449440 totatives.
8604792 has a triangular digit sum 36 in base 10.
8604792 is the difference of 2 nonnegative squares in 30 ways.
8604792 = 442 + 1342 + 29302 is the sum of 3 positive squares.
86047922 is the sum of 3 positive squares.
8604792 is a divisor of 109718 - 1.
8604792 = '860479' + '2' is the concatenation of 2 prime numbers.

Saturday, June 4, 2016

Number of the day: 51097333225

Properties of the number 51097333225:

51097333225 = 52 × 43 × 47532403 is composite and not squarefree.
51097333225 has 3 distinct prime factors, 12 divisors, 35 antidivisors and 39927217680 totatives.
Reversing the decimal digits of 51097333225 results in a semiprime.
51097333225 = 255486666132 - 255486666122 = 51097333252 - 51097333202 = 10219466772 - 10219466522 = 5941550592 - 5941550162 = 1188311152 - 1188309002 = 237667392 - 237656642 is the difference of 2 nonnegative squares in 6 ways.
51097333225 is the difference of 2 positive pentagonal numbers in 6 ways.
51097333225 = 15002 + 21492 + 2260322 is the sum of 3 positive squares.
510973332252 = 306583999352 + 408778665802 = 143072533032 + 490534398962 is the sum of 2 positive squares in 2 ways.
510973332252 is the sum of 3 positive squares.
51097333225 is a divisor of 25115844134 - 1.

Friday, June 3, 2016

Number of the day: 540081213

Properties of the number 540081213:

540081213 = 3 × 7 × 19 × 197 × 6871 is the 511728804th composite number and is squarefree.
540081213 has 5 distinct prime factors, 32 divisors, 41 antidivisors and 290848320 totatives.
540081213 is the difference of 2 nonnegative squares in 16 ways.
540081213 is the sum of 2 positive triangular numbers.
540081213 is the difference of 2 positive pentagonal numbers in 7 ways.
540081213 = 1482 + 6532 + 232302 is the sum of 3 positive squares.
5400812132 = 767628122 + 5345981552 is the sum of 2 positive squares in 1 way.
5400812132 is the sum of 3 positive squares.
540081213 is a divisor of 17592748 - 1.

Wednesday, June 1, 2016

Number of the day: 59854

Properties of the number 59854:

59854 = 2 × 29927 is semiprime and squarefree.
59854 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 29926 totatives.
59854 has an emirp digit sum 31 in base 10.
Reversing the decimal digits of 59854 results in a sphenic number.
59854 is the sum of 2 positive triangular numbers.
59854 is the difference of 2 positive pentagonal numbers in 2 ways.
59854 = 632 + 1422 + 1892 is the sum of 3 positive squares.
598542 is the sum of 3 positive squares.
59854 is a divisor of 47913 - 1.
59854 is an emirpimes in (at least) the following bases: 2, 4, 7, 8, 9, 13, 15, 19, 20, 31, 37, 38, 39, 40, 42, 44, 52, 55, 56, 58, 65, 70, 73, 76, 78, 79, 80, 85, 87, 88, 95, and 100.
59854 is palindromic in (at least) the following bases: 41, 64, and -49.
59854 in base 41 = ZOZ and consists of only the digits 'O' and 'Z'.
59854 in base 48 = Pkk and consists of only the digits 'P' and 'k'.

The number 59854 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A042016: Numerators of continued fraction convergents to sqrt(532).
A192962: Constant term of the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.
A226393: Number of nondecreasing -2..2 vectors of length n whose dot product with some nonincreasing -2..2 vector equals n