Monday, July 31, 2017

Number of the day: 741593

Properties of the number 741593:

741593 is a cyclic number.
741593 is the 59644th prime.
741593 has 31 antidivisors and 741592 totatives.
741593 has a prime digit sum 29 in base 10.
Reversing the decimal digits of 741593 results in an emirp.
741593 = 543 + 583 + 733 is the sum of 3 positive cubes in 1 way.
741593 = 3707972 - 3707962 is the difference of 2 nonnegative squares in 1 way.
741593 is the sum of 2 positive triangular numbers.
741593 is the difference of 2 positive pentagonal numbers in 1 way.
741593 = 4522 + 7332 is the sum of 2 positive squares in 1 way.
741593 = 122 + 432 + 8602 is the sum of 3 positive squares.
7415932 = 3329852 + 6626322 is the sum of 2 positive squares in 1 way.
7415932 is the sum of 3 positive squares.
741593 is a proper divisor of 4792699 - 1.
741593 = '7' + '41593' is the concatenation of 2 prime numbers.
741593 = '7415' + '93' is the concatenation of 2 semiprime numbers.
741593 is an emirp in (at least) the following bases: 7, 10, 18, 26, 28, 40, 49, 55, 57, 76, 84, 85, 88, 93, and 94.

Sunday, July 30, 2017

Number of the day: 88655022

Properties of the number 88655022:

88655022 = 2 × 32 × 421 × 11699 is the 83511370th composite number and is not squarefree.
88655022 has 4 distinct prime factors, 24 divisors, 41 antidivisors and 29478960 totatives.
88655022 has a triangular digit sum 36 in base 10.
88655022 is the sum of 2 positive triangular numbers.
88655022 is the difference of 2 positive pentagonal numbers in 3 ways.
88655022 = 3382 + 4872 + 93972 is the sum of 3 positive squares.
886550222 = 61068782 + 884444402 is the sum of 2 positive squares in 1 way.
886550222 is the sum of 3 positive squares.
88655022 is a proper divisor of 166317547 - 1.

Saturday, July 29, 2017

Number of the day: 4604

Properties of the number 4604:

4604 = 22 × 1151 is the 3980th composite number and is not squarefree.
4604 has 2 distinct prime factors, 6 divisors, 15 antidivisors and 2300 totatives.
4604 has a semiprime digit sum 14 in base 10.
4604 = 11522 - 11502 is the difference of 2 nonnegative squares in 1 way.
4604 is the difference of 2 positive pentagonal numbers in 1 way.
4604 is not the sum of 3 positive squares.
46042 is the sum of 3 positive squares.
4604 is a proper divisor of 68310 - 1.
4604 is palindromic in (at least) the following bases: 18, -43, and -59.
4604 in base 17 = ffe and consists of only the digits 'e' and 'f'.
4604 in base 18 = e3e and consists of only the digits '3' and 'e'.

The number 4604 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A004112: Numbers n where |cos(n)| (or |cosec(n)| or |cot(n)|) decreases monotonically to 0; also |tan(n)|, |sec(n)|, |sin(n)| increases.
A046964: Sin(n) decreases monotonically to -1.
A054098: Triangular array generated by its row sums: T(n,0)=1 for n >= 0, T(1,1)=2, T(n,k)=T(n,k-1)+d*r(n-k) for k=2,3,...,n, d=(-1)^(k+1), n >= 2, r(h)=sum of the numbers in row h of T.
A065850: Let u be any string of n digits from {0,...,8}; let f(u) = number of distinct primes, not beginning with 0, formed by permuting the digits of u; then a(n) = max_u f(u).
A066857: Smallest number k such that n! - k is a square
A085329: Non-palindromic solutions to sigma(Rev(n)) = sigma(n).
A139479: Numbers n such that 24n+7 belongs to A000043.
A156167: Numbers n such that n![7]-1 is prime (where n![7] = A114799(n) = septuple factorial).
A220681: T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without consecutive collinear links
A237834: Number of partitions of n such that (greatest part) - (least part) >= number of parts.

Thursday, July 27, 2017

Number of the day: 9842

Properties of the number 9842:

9842 = 2 × 7 × 19 × 37 is the 8627th composite number and is squarefree.
9842 has 4 distinct prime factors, 16 divisors, 21 antidivisors and 3888 totatives.
9842 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 9842 results in a semiprime.
9842 = 42 + 52 + 992 is the sum of 3 positive squares.
98422 = 31922 + 93102 is the sum of 2 positive squares in 1 way.
98422 is the sum of 3 positive squares.
9842 is a proper divisor of 15974 - 1.
9842 = '9' + '842' is the concatenation of 2 semiprime numbers.
9842 is palindromic in (at least) the following bases: 26, 29, 60, -3, -27, -80, and -82.
9842 in base 3 = 111111112 and consists of only the digits '1' and '2'.
9842 in base 24 = h22 and consists of only the digits '2' and 'h'.
9842 in base 26 = eee and consists of only the digit 'e'.
9842 in base 27 = dde and consists of only the digits 'd' and 'e'.
9842 in base 29 = bkb and consists of only the digits 'b' and 'k'.
9842 in base 37 = 770 and consists of only the digits '0' and '7'.
9842 in base 40 = 662 and consists of only the digits '2' and '6'.
9842 in base 49 = 44g and consists of only the digits '4' and 'g'.
9842 in base 59 = 2mm and consists of only the digits '2' and 'm'.
9842 in base 60 = 2i2 and consists of only the digits '2' and 'i'.

The number 9842 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005581: a(n) = (n-1)*n*(n+4)/6.
A007051: a(n) = (3^n + 1)/2.
A047848: Array T read by diagonals; n-th difference of (T(k,n),T(k,n-1),...,T(k,0)) is (k+2)^(n-1), for n=1,2,3,...; k=0,1,2,...
A059934: Third step in Goodstein sequences, i.e. g(5) if g(2)=n: write g(4)=A057650(n) in hereditary representation base 4, bump to base 5, then subtract 1 to produce g(5).
A124302: Number of set partitions with at most 3 blocks; number of Dyck paths of height at most 4; dimension of space of symmetric polynomials in 3 noncommuting variables.
A191450: Dispersion of (3n-1), read by antidiagonals.
A243066: Permutation of natural numbers, the even bisection of A241909 incremented by one and halved; equally, a composition of A241909 and A048673: a(n) = A048673(A241909(n)).
A243506: Permutation of natural numbers: a(n) = A048673(A122111(n)).
A254051: Square array A by downward antidiagonals: A(n,k) = (3 + 3^n*(2*floor(3*k/2) - 1))/6, n,k >= 1; read as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...
A278984: Array read by antidiagonals downwards: T(b,n) = number of words of length n over an alphabet of size b that are in standard order.

Wednesday, July 26, 2017

Number of the day: 81140298

Properties of the number 81140298:

81140298 = 2 × 3 × 19 × 711757 is the 76408061th composite number and is squarefree.
81140298 has 4 distinct prime factors, 16 divisors, 11 antidivisors and 25623216 totatives.
81140298 has a semiprime digit sum 33 in base 10.
Reversing the decimal digits of 81140298 results in a sphenic number.
81140298 = 953 + 3083 + 3713 is the sum of 3 positive cubes in 1 way.
81140298 = 322 + 1152 + 90072 is the sum of 3 positive squares.
811402982 = 209036102 + 784014482 is the sum of 2 positive squares in 1 way.
811402982 is the sum of 3 positive squares.
81140298 is a proper divisor of 12914652 - 1.

Tuesday, July 25, 2017

Number of the day: 10956

Properties of the number 10956:

10956 = 22 × 3 × 11 × 83 is the 9625th composite number and is not squarefree.
10956 has 4 distinct prime factors, 24 divisors, 9 antidivisors and 3280 totatives.
10956 has a semiprime digit sum 21 in base 10.
10956 has a Fibonacci digit sum 21 in base 10.
10956 has a triangular digit sum 21 in base 10.
Reversing the decimal digits of 10956 results in a sphenic number.
10956 = 13 + 163 + 193 is the sum of 3 positive cubes in 1 way.
10956 = 27402 - 27382 = 9162 - 9102 = 2602 - 2382 = 1162 - 502 is the difference of 2 nonnegative squares in 4 ways.
10956 is the sum of 2 positive triangular numbers.
10956 is the difference of 2 positive pentagonal numbers in 1 way.
10956 = 342 + 702 + 702 is the sum of 3 positive squares.
109562 is the sum of 3 positive squares.
10956 is a proper divisor of 3312 - 1.
10956 is palindromic in (at least) base -47.
10956 in base 39 = 77a and consists of only the digits '7' and 'a'.
10956 in base 46 = 588 and consists of only the digits '5' and '8'.

The number 10956 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A106455: Sequence A106456 interpreted as binary numbers and converted to decimal.
A111533: Row 6 of table A111528.
A114939: Number of essentially different seating arrangements for n couples around a circular table with 2n seats avoiding spouses being neighbors and avoiding clusters of 3 persons with equal gender.
A123862: Expansion of f(q)*f(q^7)/(f(-q)*f(-q^7)) in powers of q where f() is a Ramanujan theta function.
A133242: Indices n such that A134204(n) < n.
A210860: Triangle of coefficients of polynomials u(n,x) jointly generated with A210861; see the Formula section of A210861.
A213818: Antidiagonal sums of the convolution array A213773.
A232137: T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order
A281864: Number of sets of exactly four positive integers <= n having a square element sum.
A289227: Number of ways to select 6 disjoint point triples from an n X n X n triangular point grid, each point triple forming a 2 X 2 X 2 triangle.

Monday, July 24, 2017

Number of the day: 94536

Properties of the number 94536:

94536 = 23 × 32 × 13 × 101 is the 85419th composite number and is not squarefree.
94536 has 4 distinct prime factors, 48 divisors, 15 antidivisors and 28800 totatives.
94536 has a triangular digit product 3240 in base 10.
94536 is the difference of 2 nonnegative squares in 12 ways.
94536 is the sum of 2 positive triangular numbers.
94536 is the difference of 2 positive pentagonal numbers in 3 ways.
94536 = 902 + 2942 = 302 + 3062 is the sum of 2 positive squares in 2 ways.
94536 = 162 + 742 + 2982 is the sum of 3 positive squares.
945362 = 529202 + 783362 = 363602 + 872642 = 183602 + 927362 = 187202 + 926642 is the sum of 2 positive squares in 4 ways.
945362 is the sum of 3 positive squares.
94536 is a proper divisor of 10094 - 1.
94536 = '9453' + '6' is the concatenation of 2 triangular numbers.
94536 is palindromic in (at least) the following bases: -57, and -95.
94536 in base 56 = U88 and consists of only the digits '8' and 'U'.

The number 94536 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A012698: E.g.f.: sin(arctanh(x)*log(x+1))=2/2!*x^2-3/3!*x^3+16/4!*x^4-50/5!*x^5...
A012704: arcsinh(arctanh(x)*log(x+1)) = 2/2!*x^2-3/3!*x^3+16/4!*x^4-50/5!*x^5...
A187277: Let S denote the palindromes in the language {0,1,2,...,n-1}*; a(n) = number of words of length 4 in the language SS.
A192770: Numbers n such that n^2 + 1 is divisible by precisely four distinct primes where the sum of the largest and the smallest is equal to the sum of the other two.
A195674: Numbers that are formed using their own digits and addition and seventh power operators.
A199924: Numbers n such that the sum of the largest and the smallest prime divisor of n^2 + 1 equals the sum of the other distinct prime divisors.
A215950: Numbers n > 1 such that the sum of the distinct prime divisors of n^2 + 1 that are congruent to 1 mod 8 equals the sum of the distinct prime divisors congruent to 5 mod 8.

Sunday, July 23, 2017

Number of the day: 790843

Properties of the number 790843:

790843 is a cyclic number.
790843 is the 63272th prime.
790843 has 29 antidivisors and 790842 totatives.
790843 has an emirp digit sum 31 in base 10.
Reversing the decimal digits of 790843 results in an emirp.
790843 = 3954222 - 3954212 is the difference of 2 nonnegative squares in 1 way.
790843 is the sum of 2 positive triangular numbers.
790843 is the difference of 2 positive pentagonal numbers in 1 way.
790843 = 1232 + 1552 + 8672 is the sum of 3 positive squares.
7908432 is the sum of 3 positive squares.
790843 is a proper divisor of 191339 - 1.
790843 is an emirp in (at least) the following bases: 5, 8, 10, 11, 19, 21, 23, 26, 28, 29, 30, 31, 41, 44, 54, 61, 64, 67, 76, 85, 86, 89, 94, 97, 99, and 100.

Saturday, July 22, 2017

Number of the day: 7222017

Happy Casual π Day!

Properties of the number 7222017:

7222017 is a cyclic number.
7222017 = 3 × 11 × 218849 is a sphenic number and squarefree.
7222017 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 4376960 totatives.
7222017 has a semiprime digit sum 21 in base 10.
7222017 has a Fibonacci digit sum 21 in base 10.
7222017 has a triangular digit sum 21 in base 10.
7222017 = 36110092 - 36110082 = 12036712 - 12036682 = 3282792 - 3282682 = 1094412 - 1094082 is the difference of 2 nonnegative squares in 4 ways.
7222017 is the difference of 2 positive pentagonal numbers in 2 ways.
7222017 = 532 + 2182 + 26782 is the sum of 3 positive squares.
72220172 = 30162002 + 65620172 is the sum of 2 positive squares in 1 way.
72220172 is the sum of 3 positive squares.
7222017 is a proper divisor of 3976839 - 1.

Friday, July 21, 2017

Number of the day: 1844

Properties of the number 1844:

1844 = 22 × 461 is the 1561th composite number and is not squarefree.
1844 has 2 distinct prime factors, 6 divisors, 9 antidivisors and 920 totatives.
1844 has an emirp digit sum 17 in base 10.
Reversing the decimal digits of 1844 results in a prime.
1844 = 13 + 83 + 113 is the sum of 3 positive cubes in 1 way.
1844 = 4622 - 4602 is the difference of 2 nonnegative squares in 1 way.
1844 is the difference of 2 positive pentagonal numbers in 1 way.
1844 = 202 + 382 is the sum of 2 positive squares in 1 way.
1844 = 102 + 122 + 402 is the sum of 3 positive squares.
18442 = 10442 + 15202 is the sum of 2 positive squares in 1 way.
18442 is the sum of 3 positive squares.
1844 is a proper divisor of 5094 - 1.
1844 is palindromic in (at least) the following bases: 20, -13, -14, -23, and -97.
1844 in base 13 = abb and consists of only the digits 'a' and 'b'.
1844 in base 17 = 668 and consists of only the digits '6' and '8'.
1844 in base 20 = 4c4 and consists of only the digits '4' and 'c'.
1844 in base 42 = 11c and consists of only the digits '1' and 'c'.

The number 1844 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A014561: Numbers n giving rise to prime quadruples (30n+11, 30n+13, 30n+17, 30n+19).
A024026: a(n) = 3^n - n^3.
A067979: Triangle read by rows of incomplete convolutions of Lucas numbers L(n+1) = A000204(n+1), n>=0.
A067990: Triangle A067979 with rows read backwards.
A118551: a(0)=1. a(n) = a(n-1)*2, if n is in the sequence. a(n) = a(n-1) + 1 if n is missing from the sequence.
A134619: Numbers such that the arithmetic mean of the cubes of their prime factors (taken with multiplicity) is a prime.
A138920: Indices k such that A020509(k)=Phi[k](-10) is prime, where Phi is a cyclotomic polynomial.
A138940: Indices n such that A019328(n) = Phi(n,10) is prime, where Phi is a cyclotomic polynomial.
A181470: Numbers n such that 97 is the largest prime factor of n^2-1.
A265067: Coordination sequence for (2,5,8) tiling of hyperbolic plane.

Thursday, July 20, 2017

Number of the day: 6052

Properties of the number 6052:

6052 = 22 × 17 × 89 is the 5262th composite number and is not squarefree.
6052 has 3 distinct prime factors, 12 divisors, 23 antidivisors and 2816 totatives.
6052 has an emirp digit sum 13 in base 10.
6052 has a Fibonacci digit sum 13 in base 10.
Reversing the decimal digits of 6052 results in a sphenic number.
6052 = (53 × 54)/2 + … + (56 × 57)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
6052 = 15142 - 15122 = 1062 - 722 is the difference of 2 nonnegative squares in 2 ways.
6052 is the difference of 2 positive pentagonal numbers in 1 way.
6052 = 542 + 562 = 242 + 742 is the sum of 2 positive squares in 2 ways.
6052 = 342 + 362 + 602 is the sum of 3 positive squares.
60522 = 28482 + 53402 = 2202 + 60482 = 35522 + 49002 = 26522 + 54402 is the sum of 2 positive squares in 4 ways.
60522 is the sum of 3 positive squares.
6052 is a proper divisor of 11234 - 1.
6052 is palindromic in (at least) the following bases: 36, 50, 55, 88, -31, -42, and -55.
6052 in base 6 = 44004 and consists of only the digits '0' and '4'.
6052 in base 27 = 884 and consists of only the digits '4' and '8'.
6052 in base 35 = 4ww and consists of only the digits '4' and 'w'.
6052 in base 36 = 4o4 and consists of only the digits '4' and 'o'.
6052 in base 49 = 2PP and consists of only the digits '2' and 'P'.
6052 in base 50 = 2L2 and consists of only the digits '2' and 'L'.
6052 in base 54 = 244 and consists of only the digits '2' and '4'.
6052 in base 55 = 202 and consists of only the digits '0' and '2'.

The number 6052 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006128: Total number of parts in all partitions of n. Also, sum of largest parts of all partitions of n.
A018813: Number of lines through exactly 6 points of an n X n grid of points.
A028305: Triangle of numbers of permutations eliminating just k cards out of n in game of Mousetrap.
A101709: Number of partitions of n having nonnegative even rank (the rank of a partition is the largest part minus the number of parts).
A108099: a(n) = 8n^2 + 8n + 4.
A122919: Inverse of Riordan array (1/(1+x+x^2),x/(1+x)^2).
A237832: Number of partitions of n such that (greatest part) - (least part) = number of parts.
A244385: Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + ... + n^37 is prime.
A272423: Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 473", based on the 5-celled von Neumann neighborhood.
A277449: Numbers n such that there is exactly one nontrivial square n-gonal number.

Wednesday, July 19, 2017

Number of the day: 4274

Properties of the number 4274:

4274 = 2 × 2137 is semiprime and squarefree.
4274 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 2136 totatives.
4274 has an emirp digit sum 17 in base 10.
4274 has sum of divisors equal to 6414 which is a sphenic number.
4274 = 72 + 652 is the sum of 2 positive squares in 1 way.
4274 = 152 + 322 + 552 is the sum of 3 positive squares.
42742 = 9102 + 41762 is the sum of 2 positive squares in 1 way.
42742 is the sum of 3 positive squares.
4274 is a proper divisor of 26389 - 1.
4274 = '4' + '274' is the concatenation of 2 semiprime numbers.
4274 is an emirpimes in (at least) the following bases: 3, 4, 13, 14, 16, 17, 25, 27, 28, 29, 31, 34, 35, 36, 38, 39, 44, 45, 52, 56, 57, 61, 64, 68, 69, 70, 73, 75, 80, 87, 89, 91, 94, 97, and 99.
4274 is palindromic in (at least) the following bases: -35, and -48.

The number 4274 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A007498: Unique period lengths of primes mentioned in A007615.
A051627: Periods associated with A040017.
A125754: Numbers n whose reverse binary representation has the following property: let a 0 mean "halving" and a 1 mean "k -> 3k+1". The number describes an operation k -> f_n(k). If the equation f_n(k) = k has an integer solution, n is a term in the sequence.
A125756: Numbers n whose reverse binary representation has the following property: let a 0 mean "halving" and a 1 mean "k -> 3k+1". The number describes an operation k -> f_n(k). If the equation f_n(k) = k has a positive integer solution, n is a term in the sequence.
A138940: Indices n such that A019328(n) = Phi(n,10) is prime, where Phi is a cyclotomic polynomial.
A201077: G.f.: 1 / Product_{i>=1} (1-q^(2*i-1))^2*(1-q^(12*i-8))*(1-q^(12*i-6))*(1-q^(12*i-4))*(1-q^(12*i)).
A217891: T(n,k)=Number of n element 1..n arrays with each element the minimum of k adjacent elements of a permutation of 1..n+k-1 of n+k-1 elements
A267167: Growth series for affine Coxeter group B_4.
A275188: Positions of 8 in A274640.
A278784: Numbers n such that A000041(n) is of the form 2^7 * k for odd k.

Tuesday, July 18, 2017

Number of the day: 3045

Properties of the number 3045:

3045 = 3 × 5 × 7 × 29 is the 2608th composite number and is squarefree.
3045 has 4 distinct prime factors, 16 divisors, 15 antidivisors and 1344 totatives.
3045 has an oblong digit sum 12 in base 10.
Reversing the decimal digits of 3045 results in a semiprime.
3045 = 15232 - 15222 = 5092 - 5062 = 3072 - 3022 = 2212 - 2142 = 1092 - 942 = 832 - 622 = 672 - 382 = 612 - 262 is the difference of 2 nonnegative squares in 8 ways.
3045 is the sum of 2 positive triangular numbers.
3045 is the difference of 2 positive pentagonal numbers in 3 ways.
3045 = 202 + 232 + 462 is the sum of 3 positive squares.
30452 = 21002 + 22052 = 3572 + 30242 = 5042 + 30032 = 18272 + 24362 is the sum of 2 positive squares in 4 ways.
30452 is the sum of 3 positive squares.
3045 is a proper divisor of 3492 - 1.
3045 is palindromic in (at least) base 86.
3045 in base 12 = 1919 and consists of only the digits '1' and '9'.
3045 in base 14 = 1177 and consists of only the digits '1' and '7'.
3045 in base 19 = 885 and consists of only the digits '5' and '8'.
3045 in base 22 = 669 and consists of only the digits '6' and '9'.
3045 in base 27 = 44l and consists of only the digits '4' and 'l'.

The number 3045 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000266: E.g.f. exp(-x^2/2) / (1-x).
A005476: a(n) = n*(5*n - 1)/2.
A007059: Number of balanced ordered trees with n nodes.
A022289: a(n) = n*(31*n + 1)/2.
A024966: 7 times triangular numbers: 7n(n+1)/2.
A034828: a(n) = [n^2/4]*n/2.
A055561: Numbers n such that there are precisely 3 groups of order n.
A079500: Number of compositions of the integer n in which the first part is >= the other parts.
A094416: Array read by antidiagonals: generalized ordered Bell numbers Bo(r,n).
A128396: Numbers n such that n^2 divides 16^n-1.

Monday, July 17, 2017

Number of the day: 7172017

Happy Yellow Pig Day!

Properties of the number 7172017:

7172017 is a cyclic number.
7172017 = 1877 × 3821 is semiprime and squarefree.
7172017 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 7166320 totatives.
7172017 has a semiprime digit sum 25 in base 10.
Reversing the decimal digits of 7172017 results in a sphenic number.
7172017 = 35860092 - 35860082 = 28492 - 9722 is the difference of 2 nonnegative squares in 2 ways.
7172017 is the sum of 2 positive triangular numbers.
7172017 is the difference of 2 positive pentagonal numbers in 1 way.
7172017 = 12642 + 23612 = 4442 + 26412 is the sum of 2 positive squares in 2 ways.
7172017 = 862 + 1892 + 26702 is the sum of 3 positive squares.
71720172 = 43865082 + 56741852 = 39766252 + 59686082 = 23452082 + 67777452 = 22899402 + 67966172 is the sum of 2 positive squares in 4 ways.
71720172 is the sum of 3 positive squares.
7172017 is a proper divisor of 137764 - 1.
7172017 is an emirpimes in (at least) the following bases: 2, 8, 13, 19, 21, 22, 25, 26, 27, 31, 34, 35, 37, 38, 39, 44, 45, 51, 53, 59, 61, 67, 73, 75, 77, 80, 82, 83, 85, 87, 89, 91, 93, and 97.

Sunday, July 16, 2017

Number of the day: 81813

Properties of the number 81813:

81813 = 3 × 27271 is semiprime and squarefree.
81813 has 2 distinct prime factors, 4 divisors, 33 antidivisors and 54540 totatives.
81813 has a semiprime digit sum 21 in base 10.
81813 has a Fibonacci digit sum 21 in base 10.
81813 has a triangular digit sum 21 in base 10.
Reversing the decimal digits of 81813 results in a sphenic number.
81813 = 409072 - 409062 = 136372 - 136342 is the difference of 2 nonnegative squares in 2 ways.
81813 is the sum of 2 positive triangular numbers.
81813 is the difference of 2 positive pentagonal numbers in 1 way.
81813 is the difference of 2 positive pentagonal pyramidal numbers in 1 way.
81813 = 12 + 42 + 2862 is the sum of 3 positive squares.
818132 is the sum of 3 positive squares.
81813 is a proper divisor of 190154 - 1.
81813 is an emirpimes in (at least) the following bases: 3, 6, 7, 9, 15, 19, 33, 35, 48, 51, 55, 61, 67, 71, 78, 81, 85, and 99.
81813 is palindromic in (at least) base -55.
81813 in base 54 = S33 and consists of only the digits '3' and 'S'.

The number 81813 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A053948: Numbers n such that n^2 contains only digits {3,6,9}.
A137041: Numbers n such that n and the square of n use only the digits 1, 3, 6, 8 and 9.

Saturday, July 15, 2017

Number of the day: 3509167

Properties of the number 3509167:

3509167 is a cyclic number.
3509167 = 19 × 184693 is semiprime and squarefree.
3509167 has 2 distinct prime factors, 4 divisors, 27 antidivisors and 3324456 totatives.
3509167 has an emirp digit sum 31 in base 10.
Reversing the decimal digits of 3509167 results in a sphenic number.
3509167 = 17545842 - 17545832 = 923562 - 923372 is the difference of 2 nonnegative squares in 2 ways.
3509167 is the sum of 2 positive triangular numbers.
3509167 is the difference of 2 positive pentagonal numbers in 2 ways.
3509167 is not the sum of 3 positive squares.
35091672 = 21343082 + 27854952 is the sum of 2 positive squares in 1 way.
35091672 is the sum of 3 positive squares.
3509167 is a proper divisor of 3730782 - 1.
3509167 is an emirpimes in (at least) the following bases: 4, 6, 11, 13, 24, 25, 26, 31, 38, 42, 43, 44, 45, 47, 53, 55, 58, 64, 71, 76, 81, 83, 86, 87, 93, 95, 99, and 100.

The number 3509167 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A159339: Transform of A056594 by the T_{1,0} transformation (see link)

Friday, July 14, 2017

Number of the day: 96063

Properties of the number 96063:

96063 is a cyclic number.
96063 = 3 × 11 × 41 × 71 is the 86804th composite number and is squarefree.
96063 has 4 distinct prime factors, 16 divisors, 31 antidivisors and 56000 totatives.
Reversing the decimal digits of 96063 results in a sphenic number.
96063 = 480322 - 480312 = 160122 - 160092 = 43722 - 43612 = 14722 - 14392 = 11922 - 11512 = 7122 - 6412 = 4522 - 3292 = 3322 - 1192 is the difference of 2 nonnegative squares in 8 ways.
96063 is the sum of 2 positive triangular numbers.
96063 is the difference of 2 positive pentagonal numbers in 4 ways.
96063 is not the sum of 3 positive squares.
960632 = 210872 + 937202 is the sum of 2 positive squares in 1 way.
960632 is the sum of 3 positive squares.
96063 is a proper divisor of 28310 - 1.
96063 is palindromic in (at least) the following bases: 85, and -62.
96063 in base 61 = Pnn and consists of only the digits 'P' and 'n'.

The number 96063 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A115132: Partial sums of A064059.
A123789: Number of ways, counted up to symmetry, to build a contiguous building with n LEGO blocks of size 1x5 which is flat, i.e. with all blocks in parallel position and symmetric after a rotation by 180 degrees.

Wednesday, July 12, 2017

Number of the day: 378349

Properties of the number 378349:

378349 is a cyclic number.
378349 = 67 × 5647 is semiprime and squarefree.
378349 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 372636 totatives.
378349 has a semiprime digit sum 34 in base 10.
378349 has a Fibonacci digit sum 34 in base 10.
Reversing the decimal digits of 378349 results in an emirpimes.
378349 = (71 × 72)/2 + … + (137 × 138)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
378349 = 1891752 - 1891742 = 28572 - 27902 is the difference of 2 nonnegative squares in 2 ways.
378349 is the sum of 2 positive triangular numbers.
378349 is the difference of 2 positive pentagonal numbers in 2 ways.
378349 = 722 + 772 + 6062 is the sum of 3 positive squares.
3783492 is the sum of 3 positive squares.
378349 is a proper divisor of 85333 - 1.
378349 = '37834' + '9' is the concatenation of 2 semiprime numbers.
378349 is an emirpimes in (at least) the following bases: 2, 10, 11, 12, 16, 18, 26, 27, 28, 32, 34, 42, 43, 45, 46, 47, 51, 55, 58, 60, 62, 63, 64, 65, 67, 69, 70, 71, 73, 75, 83, 91, 93, 94, 96, 97, and 100.
378349 is palindromic in (at least) base -92.

Tuesday, July 11, 2017

Number of the day: 1437

Properties of the number 1437:

1437 is a cyclic number.
1437 = 3 × 479 is semiprime and squarefree.
1437 has 2 distinct prime factors, 4 divisors, 13 antidivisors and 956 totatives.
1437 has an emirpimes digit sum 15 in base 10.
1437 has a triangular digit sum 15 in base 10.
Reversing the decimal digits of 1437 results in an emirpimes.
1437 = 7192 - 7182 = 2412 - 2382 is the difference of 2 nonnegative squares in 2 ways.
1437 is the sum of 2 positive triangular numbers.
1437 is the difference of 2 positive pentagonal numbers in 1 way.
1437 = 52 + 162 + 342 is the sum of 3 positive squares.
14372 is the sum of 3 positive squares.
1437 is a proper divisor of 7239 - 1.
1437 is an emirpimes in (at least) the following bases: 3, 4, 10, 11, 19, 20, 23, 29, 30, 33, 34, 35, 36, 37, 43, 45, 46, 47, 48, 49, 55, 59, 60, 63, 66, 67, 68, 69, 71, 73, 79, 82, 92, 93, and 99.
1437 is palindromic in (at least) the following bases: 12, and -35.
1437 in base 5 = 21222 and consists of only the digits '1' and '2'.
1437 in base 12 = 9b9 and consists of only the digits '9' and 'b'.
1437 in base 37 = 11V and consists of only the digits '1' and 'V'.

The number 1437 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A003037: Smallest number of complexity n: smallest number requiring n 1's to build using +, * and ^.
A032523: Index of first occurrence of n as a term in A001203, the continued fraction for Pi.
A051227: Bernoulli number B_{2n} has denominator 42.
A103471: Number of polyominoes without holes consisting of 5 regular unit n-gons.
A123142: Number of benzenoids with 23 hexagons, C_(2v) symmetry and containing n carbon atoms.
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.
A191723: Dispersion of A047215, (numbers >1 and congruent to 0 or 2 mod 5), by antidiagonals.
A204867: T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally exactly two different ways, and new values 0..1 introduced in row major order
A219852: T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nXk array
A250167: T(n,k)=Number of length n+1 0..k arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero

Monday, July 10, 2017

Number of the day: 21846217

Properties of the number 21846217:

21846217 is a cyclic number.
21846217 = 1621 × 13477 is semiprime and squarefree.
21846217 has 2 distinct prime factors, 4 divisors, 19 antidivisors and 21831120 totatives.
21846217 has an emirp digit sum 31 in base 10.
21846217 = 109231092 - 109231082 = 75492 - 59282 is the difference of 2 nonnegative squares in 2 ways.
21846217 is the sum of 2 positive triangular numbers.
21846217 is the difference of 2 positive pentagonal numbers in 2 ways.
21846217 = 24362 + 39892 = 2162 + 46692 is the sum of 2 positive squares in 2 ways.
21846217 = 1422 + 3032 + 46622 is the sum of 3 positive squares.
218462172 = 105120602 + 191508172 = 99780252 + 194344082 = 20170082 + 217529052 = 122353082 + 180984652 is the sum of 2 positive squares in 4 ways.
218462172 is the sum of 3 positive squares.
21846217 is a proper divisor of 43310107 - 1.
21846217 = '218' + '46217' is the concatenation of 2 semiprime numbers.
21846217 is an emirpimes in (at least) the following bases: 7, 9, 12, 14, 16, 18, 19, 29, 33, 34, 35, 38, 43, 45, 47, 50, 52, 53, 54, 61, 64, 66, 67, 73, 74, 77, 78, 82, 83, 90, 91, 97, 99, and 100.

Sunday, July 9, 2017

Number of the day: 399301

Properties of the number 399301:

399301 = 72 × 29 × 281 is the 365494th composite number and is not squarefree.
399301 has 3 distinct prime factors, 12 divisors, 19 antidivisors and 329280 totatives.
399301 has a semiprime digit sum 25 in base 10.
Reversing the decimal digits of 399301 results in a prime.
399301 = 1996512 - 1996502 = 285252 - 285182 = 68992 - 68702 = 40992 - 40502 = 10852 - 8822 = 8512 - 5702 is the difference of 2 nonnegative squares in 6 ways.
399301 is the sum of 2 positive triangular numbers.
399301 is the difference of 2 positive pentagonal numbers in 5 ways.
399301 = 3992 + 4902 = 492 + 6302 is the sum of 2 positive squares in 2 ways.
399301 = 812 + 1042 + 6182 is the sum of 3 positive squares.
3993012 = 2273602 + 3282512 = 808992 + 3910202 = 617402 + 3944992 = 2753802 + 2891492 is the sum of 2 positive squares in 4 ways.
3993012 is the sum of 3 positive squares.
399301 is a proper divisor of 18114 - 1.
399301 = '39' + '9301' is the concatenation of 2 semiprime numbers.
399301 is palindromic in (at least) base -85.

The number 399301 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A230759: Values of x such that x^2 + y^2 = 53^n with x and y coprime and 0 < x < y.

Saturday, July 8, 2017

Number of the day: 849956

Properties of the number 849956:

849956 = 22 × 103 × 2063 is the 782342th composite number and is not squarefree.
849956 has 3 distinct prime factors, 12 divisors, 15 antidivisors and 420648 totatives.
849956 has a prime digit sum 41 in base 10.
849956 = 2124902 - 2124882 = 21662 - 19602 is the difference of 2 nonnegative squares in 2 ways.
849956 is the difference of 2 positive pentagonal numbers in 1 way.
849956 = 342 + 1562 + 9082 is the sum of 3 positive squares.
8499562 is the sum of 3 positive squares.
849956 is a proper divisor of 12371031 - 1.
849956 in base 47 = 88a8 and consists of only the digits '8' and 'a'.

Friday, July 7, 2017

Number of the day: 62542

Properties of the number 62542:

62542 = 2 × 31271 is semiprime and squarefree.
62542 has 2 distinct prime factors, 4 divisors, 21 antidivisors and 31270 totatives.
62542 has a prime digit sum 19 in base 10.
Reversing the decimal digits of 62542 results in an emirpimes.
62542 is the sum of 2 positive triangular numbers.
62542 is the difference of 2 positive pentagonal numbers in 2 ways.
62542 = 102 + 212 + 2492 is the sum of 3 positive squares.
625422 is the sum of 3 positive squares.
62542 is a proper divisor of 101106 - 1.
62542 = '62' + '542' is the concatenation of 2 semiprime numbers.
62542 is an emirpimes in (at least) the following bases: 5, 6, 10, 14, 15, 16, 19, 20, 22, 26, 28, 29, 32, 35, 36, 40, 43, 53, 54, 56, 59, 64, 67, 68, 71, 73, 74, 76, 77, 82, 83, 85, 86, 87, and 90.
62542 is palindromic in (at least) the following bases: 58, -61, -74, and -81.
62542 in base 23 = 5355 and consists of only the digits '3' and '5'.
62542 in base 58 = IYI and consists of only the digits 'I' and 'Y'.
62542 in base 60 = HMM and consists of only the digits 'H' and 'M'.
62542 in base 62 = GGk and consists of only the digits 'G' and 'k'.

Thursday, July 6, 2017

Number of the day: 9357

Properties of the number 9357:

9357 is a cyclic number.
9357 = 3 × 3119 is semiprime and squarefree.
9357 has 2 distinct prime factors, 4 divisors, 9 antidivisors and 6236 totatives.
Reversing the decimal digits of 9357 results in a sphenic number.
9357 = 46792 - 46782 = 15612 - 15582 is the difference of 2 nonnegative squares in 2 ways.
9357 is the difference of 2 positive pentagonal numbers in 1 way.
9357 = 112 + 202 + 942 is the sum of 3 positive squares.
93572 is the sum of 3 positive squares.
9357 is a proper divisor of 131559 - 1.
9357 = '93' + '57' is the concatenation of 2 semiprime numbers.
9357 is an emirpimes in (at least) the following bases: 2, 3, 6, 9, 11, 22, 25, 27, 28, 32, 36, 42, 50, 51, 54, 55, 57, 59, 60, 67, 74, 78, 87, 89, 93, 97, 98, 99, and 100.
9357 is palindromic in (at least) base 47.
9357 in base 22 = j77 and consists of only the digits '7' and 'j'.
9357 in base 36 = 77x and consists of only the digits '7' and 'x'.
9357 in base 46 = 4JJ and consists of only the digits '4' and 'J'.
9357 in base 47 = 4B4 and consists of only the digits '4' and 'B'.

The number 9357 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A050969: Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 20.
A076623: Total number of left truncatable primes (without zeros) in base n.
A114615: Starting numbers for which the RATS sequence has eventual period 14.
A138990: a(n) = Frobenius number for 4 successive primes = F[p(n),p(n+1),p(n+2),p(n+3)].
A142462: Triangle read by rows: T(n,k) (1<=k<=n) given by T(n, 1) = T(n,n) = 1, otherwise T(n, k) = (m*n-m*k+1)*T(n-1,k-1)+(m*k-m+1)*T(n-1,k), where m = 7.
A155121: 2*n*(1+n+n^2+n^3)-3.
A182708: a(n)=A046746(n)-A000041(n-1). Sum of the smallest parts of all partitions of n that do not contain 1 as a part.
A224956: Number of partitions of n where the difference between consecutive parts is at most 2.
A238553: Numbers n such that the decimal expansions of both n and n^2 have 3 as the digit with the smallest value and 9 as the digit with the largest value.
A262508: Numbers that occur only once in A155043; positions of zeros in A262505, ones in A262507.

Wednesday, July 5, 2017

Number of the day: 991735

Properties of the number 991735:

991735 is a cyclic number.
991735 = 5 × 198347 is semiprime and squarefree.
991735 has 2 distinct prime factors, 4 divisors, 27 antidivisors and 793384 totatives.
991735 has a semiprime digit sum 34 in base 10.
991735 has a Fibonacci digit sum 34 in base 10.
991735 = 4958682 - 4958672 = 991762 - 991712 is the difference of 2 nonnegative squares in 2 ways.
991735 is the difference of 2 positive pentagonal numbers in 2 ways.
991735 is not the sum of 3 positive squares.
9917352 = 5950412 + 7933882 is the sum of 2 positive squares in 1 way.
9917352 is the sum of 3 positive squares.
991735 is a proper divisor of 1199173 - 1.
991735 = '99173' + '5' is the concatenation of 2 prime numbers.
991735 = '9917' + '35' is the concatenation of 2 semiprime numbers.
991735 is an emirpimes in (at least) the following bases: 5, 8, 13, 15, 17, 20, 23, 28, 34, 35, 37, 39, 53, 56, 57, 59, 61, 65, 70, 71, 79, 80, 83, 85, 87, 88, 90, and 98.

Monday, July 3, 2017

Number of the day: 639918

Properties of the number 639918:

639918 = 2 × 32 × 73 × 487 is the 587849th composite number and is not squarefree.
639918 has 4 distinct prime factors, 24 divisors, 29 antidivisors and 209952 totatives.
639918 has a triangular digit sum 36 in base 10.
639918 is the sum of 2 positive triangular numbers.
639918 = 622 + 852 + 7932 is the sum of 3 positive squares.
6399182 = 4207682 + 4821302 is the sum of 2 positive squares in 1 way.
6399182 is the sum of 3 positive squares.
639918 is a proper divisor of 4118 - 1.

Sunday, July 2, 2017

Number of the day: 6728971752

Properties of the number 6728971752:

6728971752 = 23 × 33 × 19 × 1639613 is the 6417133092th composite number and is not squarefree.
6728971752 has 4 distinct prime factors, 64 divisors, 19 antidivisors and 2124937152 totatives.
6728971752 = 8523 + 11783 + 16483 = 1803 + 11783 + 17203 is the sum of 3 positive cubes in 2 ways.
6728971752 is the difference of 2 nonnegative squares in 16 ways.
6728971752 is the difference of 2 positive pentagonal numbers in 4 ways.
6728971752 = 262 + 2242 + 820302 is the sum of 3 positive squares.
67289717522 = 39007494002 + 54829932482 is the sum of 2 positive squares in 1 way.
67289717522 is the sum of 3 positive squares.
6728971752 is a proper divisor of 1747189186 - 1.

Saturday, July 1, 2017

Number of the day: 890905

Gottfried Wilhelm Leibniz was born on this day 371 years ago.

Properties of the number 890905:

890905 = 5 × 23 × 61 × 127 is the 820289th composite number and is squarefree.
890905 has 4 distinct prime factors, 16 divisors, 23 antidivisors and 665280 totatives.
890905 has an emirp digit sum 31 in base 10.
Reversing the decimal digits of 890905 results in a sphenic number.
890905 = 4454532 - 4454522 = 890932 - 890882 = 193792 - 193562 = 73332 - 72722 = 39312 - 38162 = 35712 - 34442 = 16132 - 13082 = 10192 - 3842 is the difference of 2 nonnegative squares in 8 ways.
890905 is the difference of 2 positive pentagonal numbers in 7 ways.
890905 = 252 + 542 + 9422 is the sum of 3 positive squares.
8909052 = 3972562 + 7974332 = 1606552 + 8763002 = 6046472 + 6543042 = 5345432 + 7127242 is the sum of 2 positive squares in 4 ways.
8909052 is the sum of 3 positive squares.
890905 is a proper divisor of 128960 - 1.
890905 is palindromic in (at least) base -56.