Number of the day: 25304290

Carl Friedrich Gauss was born on this day 241 years ago.

Claude Shannon was born on this day 102 years ago.

Properties of the number 25304290:

25304290 = 2 × 5 × 11 × 461 × 499 is the 23720583^th composite number and is squarefree.
25304290 has 5 distinct prime factors, 32 divisors, 23 antidivisors and 9163200 totatives.
25304290 has a semiprime digit sum 25 in base 10.
25304290 = 101³ + 104³ + 285³ is the sum of 3 positive cubes in 1 way.
25304290 is the difference of 2 positive pentagonal numbers in 7 ways.
25304290 = 211² + 360² + 5013² is the sum of 3 positive squares.
25304290² = 15182574² + 20243432² = 1053888² + 25282334² = 8090786² + 23975952² = 14326290² + 20858200² is the sum of 2 positive squares in 4 ways.
25304290² is the sum of 3 positive squares.
25304290 is a proper divisor of 997²⁰ - 1.

Number of the day: 1663

Henri Poincaré was born on this day 164 years ago.

Properties of the number 1663:

1663 is a cyclic number.
1663 is the 261^th prime.
1663 has 13 antidivisors and 1662 totatives.
Reversing the decimal digits of 1663 results in a semiprime.
1663 = 832² - 831² is the difference of 2 nonnegative squares in 1 way.
1663 is the sum of 2 positive triangular numbers.
1663 is the difference of 2 positive pentagonal numbers in 1 way.
1663 is not the sum of 3 positive squares.
1663² is the sum of 3 positive squares.
1663 is a proper divisor of 41²⁷⁷ - 1.
1663 is an emirp in (at least) the following bases: 4, 12, 18, 19, 25, 30, 32, 34, 36, 41, 47, 49, 50, 51, 52, 53, 56, 57, 59, 63, 64, 66, 67, 70, 71, 75, 76, 79, 83, 84, 85, 91, and 93.
1663 is palindromic in (at least) the following bases: 6, and -21.
1663 in base 6 = 11411 and consists of only the digits '1' and '4'.
1663 in base 20 = 433 and consists of only the digits '3' and '4'.
1663 in base 23 = 337 and consists of only the digits '3' and '7'.
1663 in base 40 = 11N and consists of only the digits '1' and 'N'.

The number 1663 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A007529: Prime triples: n; n+2 or n+4; n+6 all prime.
A007658: Numbers n such that (3^n + 1)/4 is prime.
A007690: Number of partitions of n in which no part occurs just once.
A022005: Initial members of prime triples (p, p+4, p+6).
A059802: Numbers n such that 5^n - 4^n is prime.
A127576: Primes of the form 16n+15.
A140633: Primes of the form 7x^2+4xy+52y^2.
A161206: V-toothpick (or honeycomb) sequence (see Comments lines for definition).
A187220: Gullwing sequence (see Comments lines for precise definition).
A235394: Primes whose decimal representation is a valid number in base 8 and interpreted as such is again a prime.

Number of the day: 17476

Properties of the number 17476:

17476 = 2² × 17 × 257 is the 15466^th composite number and is not squarefree.
17476 has 3 distinct prime factors, 12 divisors, 11 antidivisors and 8192 totatives.
17476 has a semiprime digit sum 25 in base 10.
17476 has a triangular digit product 1176 in base 10.
Reversing the decimal digits of 17476 results in a semiprime.
17476 = 4370² - 4368² = 274² - 240² is the difference of 2 nonnegative squares in 2 ways.
17476 is the difference of 2 positive pentagonal numbers in 1 way.
17476 = 40² + 126² = 24² + 130² is the sum of 2 positive squares in 2 ways.
17476 = 4² + 6² + 132² is the sum of 3 positive squares.
17476² = 10080² + 14276² = 8224² + 15420² = 6240² + 16324² = 2176² + 17340² is the sum of 2 positive squares in 4 ways.
17476² is the sum of 3 positive squares.
17476 is a proper divisor of 1543⁴ - 1.
17476 is palindromic in (at least) the following bases: 16, 37, 41, and 64.
17476 in base 4 = 10101010 and consists of only the digits '0' and '1'.
17476 in base 16 = 4444 and consists of only the digit '4'.
17476 in base 37 = CSC and consists of only the digits 'C' and 'S'.
17476 in base 40 = Aaa and consists of only the digits 'A' and 'a'.
17476 in base 41 = AGA and consists of only the digits 'A' and 'G'.

The number 17476 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002956: Number of basic invariants for cyclic group of order and degree n.
A033114: Base-4 digits are, in order, the first n terms of the periodic sequence with initial period 1,0.
A083593: Expansion of 1/((1-2*x)*(1-x^4)).
A115451: Expansion of 1/((1+x)*(1-2*x)*(1+x^2)).
A240250: T(n,k)=Number of nXk 0..3 arrays with no element equal to the sum of elements to its left or the sum of the elements above it or the sum of the elements diagonally to its northwest or the sum of the elements antidiagonally to its northeast, modulo 4
A273972: 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 20", based on the 5-celled von Neumann neighborhood.
A274224: 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 22", based on the 5-celled von Neumann neighborhood.
A277933: 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 6", based on the 5-celled von Neumann neighborhood.
A281216: 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 342", based on the 5-celled von Neumann neighborhood.
A283216: 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 597", based on the 5-celled von Neumann neighborhood.

Number of the day: 73037

Properties of the number 73037:

73037 is a cyclic number.
73037 and 73039 form a twin prime pair.
73037 has 19 antidivisors and 73036 totatives.
73037 has an oblong digit sum 20 in base 10.
73037 = 19³ + 19³ + 39³ is the sum of 3 positive cubes in 1 way.
73037 = 36519² - 36518² is the difference of 2 nonnegative squares in 1 way.
73037 is the difference of 2 positive pentagonal numbers in 1 way.
73037 = 26² + 269² is the sum of 2 positive squares in 1 way.
73037 = 4² + 11² + 270² is the sum of 3 positive squares.
73037² = 13988² + 71685² is the sum of 2 positive squares in 1 way.
73037² is the sum of 3 positive squares.
73037 is a proper divisor of 647⁵⁸⁹ - 1.
73037 = '7' + '3037' is the concatenation of 2 prime numbers.
73037 is an emirp in (at least) the following bases: 4, 5, 9, 11, 13, 14, 20, 23, 28, 34, 36, 39, 40, 44, 47, 49, 54, 56, 57, 58, 61, 62, 71, 73, 74, 80, 89, 93, 96, 99, and 100.
73037 is a palindrome (in base 10).
73037 is palindromic in (at least) the following bases: 42, -46, and -61.
73037 in base 42 = fGf and consists of only the digits 'G' and 'f'.
73037 in base 60 = KHH and consists of only the digits 'H' and 'K'.

The number 73037 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A052024: Every suffix of palindromic prime a(n) is prime (left-truncatable).
A062352: Palindromic primes with strictly decreasing digits up to the middle and then strictly increasing.
A081220: Palindromic primes = 1 mod 4.
A082769: a(n) = smallest palindromic prime that begins with A082768(n), or 0 if no such number exists.
A083840: Palindromic primes which are a member of a twin prime pair.
A083841: Palindromic primes p such that p+2 is also a prime: members of A083840 which are the smaller member of a twin prime pair.
A088269: Palindromic primes that yield a prime when sandwiched between two 1's. (Prefixing and suffixing a one on both sides yields another pal prime).
A109184: Palindromic primes with digit sum 20.
A136098: Prime palindromic cyclops numbers.
A260378: Primes that contain only the digits (0, 3, 7).

Number of the day: 8442

Felix Klein was born on this day 169 years ago.

Andrey Kolmogorov was born on this day 115 years ago.

Properties of the number 8442:

8442 = 2 × 3² × 7 × 67 is the 7386^th composite number and is not squarefree.
8442 has 4 distinct prime factors, 24 divisors, 17 antidivisors and 2376 totatives.
8442 is the sum of 2 positive triangular numbers.
8442 = 11² + 20² + 89² is the sum of 3 positive squares.
8442² is the sum of 3 positive squares.
8442 is a proper divisor of 937² - 1.
8442 is palindromic in (at least) the following bases: 5, 37, -35, and -38.
8442 in base 5 = 232232 and consists of only the digits '2' and '3'.
8442 in base 20 = 1122 and consists of only the digits '1' and '2'.
8442 in base 26 = cci and consists of only the digits 'c' and 'i'.
8442 in base 34 = 7aa and consists of only the digits '7' and 'a'.
8442 in base 36 = 6ii and consists of only the digits '6' and 'i'.
8442 in base 37 = 666 and consists of only the digit '6'.

The number 8442 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001402: Number of partitions of n into at most 6 parts.
A022271: a(n) = n*(13*n + 1)/2.
A061428: Geometric mean of the digits = 4. In other words the product of the digits is = 4^k where k is the number of digits.
A129526: Number of n-bead two-color bracelets with 00 prohibited.
A135192: Numbers n that raised to the powers from 1 to k (with k>=1) are multiple of the sum of their digits (n raised to k+1 must not be a multiple). Case k=7.
A143860: Ulam's spiral (NNW spoke).
A161407: Number of partitions of n^2 into parts smaller than n.
A172179: (1,[99n+1]) Pascal Triangle.
A235497: 2n concatenated with n.
A299287: Coordination sequence for "tcd" 3D uniform tiling.

Number of the day: 42561

Properties of the number 42561:

42561 = 3² × 4729 is the 38110^th composite number and is not squarefree.
42561 has 2 distinct prime factors, 6 divisors, 7 antidivisors and 28368 totatives.
42561 has an oblong digit product 240 in base 10.
42561 = 17³ + 22³ + 30³ is the sum of 3 positive cubes in 1 way.
42561 = 21281² - 21280² = 7095² - 7092² = 2369² - 2360² is the difference of 2 nonnegative squares in 3 ways.
42561 is the difference of 2 positive pentagonal numbers in 1 way.
42561 = 135² + 156² is the sum of 2 positive squares in 1 way.
42561 = 34² + 91² + 182² is the sum of 3 positive squares.
42561² = 6111² + 42120² is the sum of 2 positive squares in 1 way.
42561² is the sum of 3 positive squares.
42561 is a proper divisor of 1223⁸ - 1.
42561 = '4' + '2561' is the concatenation of 2 semiprime numbers.
42561 = '42' + '561' is the concatenation of 2 sphenic numbers.
42561 is palindromic in (at least) base -72.

The number 42561 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005225: Number of permutations of length n with equal cycles.
A132960: a(n) = n!*Sum_{d|n} (-1)^(d+1)/(d!*(n/d)^d).
A155627: 6^n-4^n+1.
A218868: Triangular array read by rows: T(n,k) is the number of n-permutations that have exactly k distinct cycle lengths.

Number of the day: 6426

Properties of the number 6426:

6426 = 2 × 3³ × 7 × 17 is the 5590^th composite number and is not squarefree.
6426 has 4 distinct prime factors, 32 divisors, 17 antidivisors and 1728 totatives.
6426 is the sum of 2 positive triangular numbers.
6426 is the difference of 2 positive pentagonal numbers in 1 way.
6426 = 16² + 29² + 73² is the sum of 3 positive squares.
6426² = 3024² + 5670² is the sum of 2 positive squares in 1 way.
6426² is the sum of 3 positive squares.
6426 is a proper divisor of 613³ - 1.
6426 is palindromic in (at least) the following bases: 38, and -73.
6426 in base 37 = 4PP and consists of only the digits '4' and 'P'.
6426 in base 38 = 4H4 and consists of only the digits '4' and 'H'.
6426 in base 56 = 22g and consists of only the digits '2' and 'g'.

The number 6426 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A014640: Even heptagonal numbers (A000566).
A033571: a(n) = (2*n + 1)*(5*n + 1).
A050047: a(n) = a(n-1)+a(m), where m=2n-2-2^(p+1) and 2^p<n-1<=2^(p+1), for n >= 4.
A073268: Number of plane binary trees whose right (or respectively: left) subtree is a unique "complete" tree of (2^m)-1 nodes with all the leaf-nodes at the same depth m and the left (or respectively: right) subtree is any plane binary tree of size n - 2^m + 1.
A078868: Decimal concatenations of the quadruples (d1,d2,d3,d4) with elements in {2,4,6} for which there exists a prime p >= 5 such that the differences between the 5 consecutive primes starting with p are (d1,d2,d3,d4).
A171256: Numbers n such that sigma(n) = 10*phi(n) (where sigma=A000203, phi=A000010).
A179670: Numbers of the form p^3*q*r*s where p, q, r, and s are distinct primes.
A241647: Numbers m such that the GCD of the x's that satisfy sigma(x)=m is 2.
A277665: 5th-order coefficients of the 1/N-expansion of traces of negative powers of real Wishart matrices with parameter c=2.
A286416: Number T(n,k) of entries in the k-th last blocks of all set partitions of [n]; triangle T(n,k), n>=1, 1<=k<=n, read by rows.

Number of the day: 8088

Properties of the number 8088:

8088 = 2³ × 3 × 337 is the 7071^th composite number and is not squarefree.
8088 has 3 distinct prime factors, 16 divisors, 9 antidivisors and 2688 totatives.
8088 = 2023² - 2021² = 1013² - 1009² = 677² - 671² = 343² - 331² is the difference of 2 nonnegative squares in 4 ways.
8088 is the sum of 2 positive triangular numbers.
8088 = 4² + 26² + 86² is the sum of 3 positive squares.
8088² = 4200² + 6912² is the sum of 2 positive squares in 1 way.
8088² is the sum of 3 positive squares.
8088 is a proper divisor of 673² - 1.
8088 is palindromic in (at least) the following bases: 23, 43, 49, -25, -47, and -55.
8088 consists of only the digits '0' and '8'.
8088 in base 23 = f6f and consists of only the digits '6' and 'f'.
8088 in base 42 = 4OO and consists of only the digits '4' and 'O'.
8088 in base 43 = 4G4 and consists of only the digits '4' and 'G'.
8088 in base 48 = 3OO and consists of only the digits '3' and 'O'.
8088 in base 49 = 3I3 and consists of only the digits '3' and 'I'.

The number 8088 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006951: Number of conjugacy classes in GL(n,2).
A035937: Number of partitions in parts not of the form 7k, 7k+1 or 7k-1. Also number of partitions with no part of size 1 and differences between parts at distance 2 are greater than 1.
A084832: Numbers n such that 2*R_n - 1 is prime, where R_n = 11...1 is the repunit (A002275) of length n.
A101198: Number of partitions of n with rank 1 (the rank of a partition is the largest part minus the number of parts).
A114615: Starting numbers for which the RATS sequence has eventual period 14.
A204095: Numbers whose set of base 10 digits is {0,8}.
A266493: T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with no element 1 greater than its north, west, northwest or northeast neighbor modulo n and the upper left element equal to 0.
A274471: Numbers missing from A134419 despite satisfying the necessary congruence conditions (see comments).
A292738: Numbers in which 8 outnumbers all other digits together.
A293100: T(n,k)=Number of nXk 0..1 arrays with the number of 1s horizontally, diagonally or antidiagonally adjacent to some 0 two less than the number of 0s adjacent to some 1.

Number of the day: 60509

Properties of the number 60509:

60509 is a cyclic number.
60509 is the 6101^th prime.
60509 has 15 antidivisors and 60508 totatives.
60509 has an oblong digit sum 20 in base 10.
60509 = 30255² - 30254² is the difference of 2 nonnegative squares in 1 way.
60509 is the sum of 2 positive triangular numbers.
60509 is the difference of 2 positive pentagonal numbers in 1 way.
60509 = 22² + 245² is the sum of 2 positive squares in 1 way.
60509 = 10² + 53² + 240² is the sum of 3 positive squares.
60509² = 10780² + 59541² is the sum of 2 positive squares in 1 way.
60509² is the sum of 3 positive squares.
60509 is a proper divisor of 53²¹⁶¹ - 1.
60509 is an emirp in (at least) the following bases: 4, 5, 6, 22, 26, 33, 38, 40, 44, 47, 58, 62, 67, 73, 77, 83, and 92.
60509 is palindromic in (at least) the following bases: 45, and 51.
60509 in base 45 = TdT and consists of only the digits 'T' and 'd'.
60509 in base 51 = NDN and consists of only the digits 'D' and 'N'.

The number 60509 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A018847: Strobogrammatic primes: the same upside down (calculator-style numerals).
A028883: Primes of form n^2 - 7.
A105378: Primes from merging of 5 successive digits in decimal expansion of Zeta(2) or (Pi^2)/6.
A201487: Primes of the form 5n^2 + 9.
A242385: Lesser of consecutive primes such that their average is of the form k*(k+2), for some integer k.
A242991: Smallest prime p such that p - floor(sqrt(p))^2 = n^2.

Number of the day: 291884

Properties of the number 291884:

291884 = 2² × 43 × 1697 is the 266506^th composite number and is not squarefree.
291884 has 3 distinct prime factors, 12 divisors, 11 antidivisors and 142464 totatives.
291884 = 72972² - 72970² = 1740² - 1654² is the difference of 2 nonnegative squares in 2 ways.
291884 is the difference of 2 positive pentagonal numbers in 2 ways.
291884 = 70² + 78² + 530² is the sum of 3 positive squares.
291884² = 56416² + 286380² is the sum of 2 positive squares in 1 way.
291884² is the sum of 3 positive squares.
291884 is a proper divisor of 1283¹² - 1.

Number of the day: 737919

Properties of the number 737919:

737919 = 3² × 7 × 13 × 17 × 53 is the 678544^th composite number and is not squarefree.
737919 has 5 distinct prime factors, 48 divisors, 53 antidivisors and 359424 totatives.
737919 has a triangular digit sum 36 in base 10.
737919 = 91² + … + 143² is the sum of at least 2 consecutive positive squares in 1 way.
737919 is the difference of 2 nonnegative squares in 24 ways.
737919 is the difference of 2 positive pentagonal numbers in 4 ways.
737919 is not the sum of 3 positive squares.
737919² = 369369² + 638820² = 95256² + 731745² = 447615² + 586656² = 347256² + 651105² = 70119² + 734580² = 467460² + 570969² = 237825² + 698544² = 49140² + 736281² = 328545² + 660744² = 389844² + 626535² = 118881² + 728280² = 428400² + 600831² = 283815² + 681156² is the sum of 2 positive squares in 13 ways.
737919² is the sum of 3 positive squares.
737919 is a proper divisor of 953⁶ - 1.
737919 = '73' + '7919' is the concatenation of 2 prime numbers.
737919 is palindromic in (at least) base -98.
737919 in base 30 = r9r9 and consists of only the digits '9' and 'r'.

Number of the day: 5508

Properties of the number 5508:

5508 = 2² × 3⁴ × 17 is the 4779^th composite number and is not squarefree.
5508 has 3 distinct prime factors, 30 divisors, 13 antidivisors and 1728 totatives.
5508 = 1378² - 1376² = 462² - 456² = 162² - 144² = 98² - 64² = 78² - 24² is the difference of 2 nonnegative squares in 5 ways.
5508 = 18² + 72² is the sum of 2 positive squares in 1 way.
5508 = 16² + 34² + 64² is the sum of 3 positive squares.
5508² = 2592² + 4860² is the sum of 2 positive squares in 1 way.
5508² is the sum of 3 positive squares.
5508 is a proper divisor of 647² - 1.
5508 is palindromic in (at least) the following bases: 25, 80, and -23.
5508 in base 18 = h00 and consists of only the digits '0' and 'h'.
5508 in base 22 = b88 and consists of only the digits '8' and 'b'.
5508 in base 25 = 8k8 and consists of only the digits '8' and 'k'.

The number 5508 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001392: a(n) = 9*binomial(2n,n-4)/(n+5).
A005557: Number of walks on square lattice.
A039599: Triangle formed from even-numbered columns of triangle of expansions of powers of x in terms of Chebyshev polynomials U_n(x).
A045991: a(n) = n^3 - n^2.
A075268: Trajectory of 442 under the Reverse and Add! operation carried out in base 2.
A179669: Products of form p^4*q^2*r where p, q and r are three distinct primes.
A187738: G.f.: Sum_{n>=0} (3*n+1)^n * x^n / (1 + (3*n+1)*x)^n.
A244630: 17*n^2.
A246099: Paradigm shift sequence for (4,5) production scheme with replacement.
A252514: T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and column sum equal to 0 2 5 6 or 7 and every 3X3 diagonal and antidiagonal sum not equal to 0 2 5 6 or 7

Number of the day: 457828718

Properties of the number 457828718:

457828718 = 2 × 10169 × 22511 is a sphenic number and squarefree.
457828718 has 3 distinct prime factors, 8 divisors, 99 antidivisors and 228881680 totatives.
Reversing the decimal digits of 457828718 results in a sphenic number.
457828718 is the difference of 2 positive pentagonal numbers in 1 way.
457828718 = 13² + 410² + 21393² is the sum of 3 positive squares.
457828718² = 117057200² + 442611282² is the sum of 2 positive squares in 1 way.
457828718² is the sum of 3 positive squares.
457828718 is a proper divisor of 733¹³⁹⁵⁶² - 1.
457828718 = '4' + '57828718' is the concatenation of 2 semiprime numbers.
457828718 = '45782' + '8718' is the concatenation of 2 sphenic numbers.

Number of the day: 163404

Leonhard Euler was born on this day 311 years ago.

Properties of the number 163404:

163404 = 2² × 3³ × 17 × 89 is the 148438^th composite number and is not squarefree.
163404 has 4 distinct prime factors, 48 divisors, 23 antidivisors and 50688 totatives.
163404 = 40852² - 40850² = 13620² - 13614² = 4548² - 4530² = 2420² - 2386² = 1540² - 1486² = 852² - 750² = 548² - 370² = 420² - 114² is the difference of 2 nonnegative squares in 8 ways.
163404 is the sum of 2 positive triangular numbers.
163404 is the difference of 2 positive pentagonal numbers in 1 way.
163404 = 38² + 82² + 394² is the sum of 3 positive squares.
163404² = 76896² + 144180² = 5940² + 163296² = 95904² + 132300² = 71604² + 146880² is the sum of 2 positive squares in 4 ways.
163404² is the sum of 3 positive squares.
163404 is a proper divisor of 433⁸ - 1.
163404 is palindromic in (at least) the following bases: 55, 56, 73, -55, -71, and -84.
163404 in base 6 = 3300300 and consists of only the digits '0' and '3'.
163404 in base 55 = s0s and consists of only the digits '0' and 's'.
163404 in base 56 = q5q and consists of only the digits '5' and 'q'.

The number 163404 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A034959: Divide even numbers into groups with prime(n) elements and add together.

Number of the day: 1166568437

Christiaan Huygens was born on this day 389 years ago.

Properties of the number 1166568437:

1166568437 is a cyclic number.
1166568437 = 1429 × 816353 is semiprime and squarefree.
1166568437 has 2 distinct prime factors, 4 divisors, 27 antidivisors and 1165750656 totatives.
1166568437 has a prime digit sum 47 in base 10.
Reversing the decimal digits of 1166568437 results in an emirpimes.
1166568437 = 583284219² - 583284218² = 408891² - 407462² is the difference of 2 nonnegative squares in 2 ways.
1166568437 is the sum of 2 positive triangular numbers.
1166568437 is the difference of 2 positive pentagonal numbers in 2 ways.
1166568437 = 22654² + 25561² = 15241² + 30566² is the sum of 2 positive squares in 2 ways.
1166568437 = 22² + 457² + 34152² is the sum of 3 positive squares.
1166568437² = 436027912² + 1082017365² = 140161005² + 1158117788² = 701992275² + 931712812² = 302866963² + 1126567140² is the sum of 2 positive squares in 4 ways.
1166568437² is the sum of 3 positive squares.
1166568437 is a proper divisor of 1627⁸⁸³⁶⁸ - 1.
1166568437 = '116656843' + '7' is the concatenation of 2 prime numbers.
1166568437 is an emirpimes in (at least) the following bases: 3, 7, 9, 10, 11, 15, 21, 25, 37, 40, 41, 44, 49, 53, 57, 58, 63, 64, 65, 67, 82, 86, 90, and 96.

Number of the day: 7868

Properties of the number 7868:

7868 = 2² × 7 × 281 is the 6874^th composite number and is not squarefree.
7868 has 3 distinct prime factors, 12 divisors, 9 antidivisors and 3360 totatives.
7868 has a prime digit sum 29 in base 10.
Reversing the decimal digits of 7868 results in a sphenic number.
7868 = 1968² - 1966² = 288² - 274² is the difference of 2 nonnegative squares in 2 ways.
7868 is the sum of 2 positive triangular numbers.
7868 is the difference of 2 positive pentagonal numbers in 2 ways.
7868 is not the sum of 3 positive squares.
7868² = 4480² + 6468² is the sum of 2 positive squares in 1 way.
7868² is the sum of 3 positive squares.
7868 is a proper divisor of 563⁶ - 1.
7868 is palindromic in (at least) the following bases: 13, 29, 30, 57, -9, -27, -55, and -69.
7868 in base 13 = 3773 and consists of only the digits '3' and '7'.
7868 in base 21 = hhe and consists of only the digits 'e' and 'h'.
7868 in base 26 = bgg and consists of only the digits 'b' and 'g'.
7868 in base 29 = 9a9 and consists of only the digits '9' and 'a'.
7868 in base 30 = 8m8 and consists of only the digits '8' and 'm'.
7868 in base 33 = 77e and consists of only the digits '7' and 'e'.
7868 in base 56 = 2SS and consists of only the digits '2' and 'S'.
7868 in base 57 = 2O2 and consists of only the digits '2' and 'O'.
7868 in base 62 = 22u and consists of only the digits '2' and 'u'.

The number 7868 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000441: a(n) = Sum_{k=1..n-1} k*sigma(k)*sigma(n-k).
A000716: Number of partitions of n into parts of 3 kinds.
A055437: a(n) = 10*n^2+n.
A065069: Numbers n such that Fibonacci(n) is not squarefree, but for all proper divisors k of n, Fibonacci(k) is squarefree.
A188774: T(n,k)=Number of nXk binary arrays without the pattern 0 1 0 vertically or horizontally
A206368: Numbers n such that A206369(n) = A206039(n+1).
A207100: T(n,k)=Number of 0..k arrays x(0..n-1) of n elements with each no smaller than the sum of its two previous neighbors modulo (k+1)
A231682: a(n) = Sum_{i=0..n} digsum_8(i)^3, where digsum_8(i) = A053829(i).
A240192: T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or three plus the sum of the elements diagonally to its northwest, modulo 4
A287055: Numbers n such that uphi(n) = uphi(n+1), where uphi(n) is the unitary totient function (A047994).

Number of the day: 5879

Properties of the number 5879:

5879 is a cyclic number.
5879 and 5881 form a twin prime pair.
5879 has 5 antidivisors and 5878 totatives.
5879 has a prime digit sum 29 in base 10.
Reversing the decimal digits of 5879 results in a sphenic number.
5879 = 2940² - 2939² is the difference of 2 nonnegative squares in 1 way.
5879 is the difference of 2 positive pentagonal numbers in 1 way.
5879 is not the sum of 3 positive squares.
5879² is the sum of 3 positive squares.
5879 is a proper divisor of 2²⁹³⁹ - 1.
5879 is an emirp in (at least) the following bases: 7, 9, 13, 16, 19, 31, 40, 45, 49, 59, 61, 68, 69, 72, 75, 85, 92, 96, 97, and 99.
5879 is palindromic in (at least) the following bases: 33, and -52.
5879 in base 32 = 5nn and consists of only the digits '5' and 'n'.
5879 in base 33 = 5d5 and consists of only the digits '5' and 'd'.

The number 5879 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A053983: a(n) = (2*n-1)*a(n-1) - a(n-2), a(0)=a(1)=1.
A073609: a(0) = 2; a(n) for n > 0 is the smallest prime greater than a(n-1) that differs from a(n-1) by a square.
A100827: Highly cototient numbers: records for a(n) in A063741.
A158713: Primes p such that p1=Ceiling[p/2]+p is prime and p2=Ceiling[p1/2]+p is prime.
A181602: Primes p such that p-1 is a semiprime and p+2 is prime or prime squared.
A181669: Primes p of the form 6n-1 such that p-1 is a semiprime and p+2 is prime or prime squared.
A186589: T(n,k)=Number of (n+3)X(k+3) 0..2 arrays with every 4X4 subblock commuting with each horizontal and vertical neighbor 4X4 subblock
A221655: T(n,k)=Number of nXk arrays of occupancy after each element moves to some horizontal, diagonal or antidiagonal neighbor, without move-in move-out left turns
A255528: G.f.: Product_{k>=1} 1/(1+x^k)^k.
A267019: T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with every element equal to or 1 greater than any northeast or northwest neighbors modulo n and the upper left element equal to 0.

Number of the day: 7839

Properties of the number 7839:

7839 = 3² × 13 × 67 is the 6848^th composite number and is not squarefree.
7839 has 3 distinct prime factors, 12 divisors, 13 antidivisors and 4752 totatives.
7839 = 9³ + 13³ + 17³ is the sum of 3 positive cubes in 1 way.
7839 = 31³ - 28³ is the difference of 2 positive cubes in 1 way.
7839 = 3920² - 3919² = 1308² - 1305² = 440² - 431² = 308² - 295² = 120² - 81² = 92² - 25² is the difference of 2 nonnegative squares in 6 ways.
7839 is the sum of 2 positive triangular numbers.
7839 is the difference of 2 positive pentagonal numbers in 1 way.
7839 is not the sum of 3 positive squares.
7839² = 3015² + 7236² is the sum of 2 positive squares in 1 way.
7839² is the sum of 3 positive squares.
7839 is a proper divisor of 937² - 1.
7839 = '7' + '839' is the concatenation of 2 prime numbers.
7839 is palindromic in (at least) the following bases: 20, 29, -2, and -30.
7839 in base 20 = jbj and consists of only the digits 'b' and 'j'.
7839 in base 28 = 9rr and consists of only the digits '9' and 'r'.
7839 in base 29 = 999 and consists of only the digit '9'.
7839 in base 62 = 22R and consists of only the digits '2' and 'R'.

The number 7839 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A033680: a(1) = 1; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.
A033681: a(1) = 3; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.
A036906: Scan decimal expansion of zeta(3) until all n-digit strings have been seen; a(n) is number of digits that must be scanned.
A055629: Beginning of first run of at least n consecutive happy numbers.
A072494: First of triples of consecutive happy numbers, i.e., the first of three consecutive integers each of which is a happy number (A007770).
A113745: Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 8 multiples of n-1, n-2, ..., 1, for n>=1.
A113747: Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 10 multiples of n-1, n-2, ..., 1, for n>=1.
A235497: 2n concatenated with n.
A241654: Number of partitions p of n such that 2*(number of even numbers in p) = (number of odd numbers in p).
A283726: T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than two of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

Number of the day: 5956

Élie Joseph Cartan was born on this day 149 years ago.

Properties of the number 5956:

5956 = 2² × 1489 is the 5174^th composite number and is not squarefree.
5956 has 2 distinct prime factors, 6 divisors, 13 antidivisors and 2976 totatives.
5956 has a semiprime digit sum 25 in base 10.
Reversing the decimal digits of 5956 results in a semiprime.
5956 = 1490² - 1488² is the difference of 2 nonnegative squares in 1 way.
5956 is the sum of 2 positive triangular numbers.
5956 is the difference of 2 positive pentagonal numbers in 1 way.
5956 = 40² + 66² is the sum of 2 positive squares in 1 way.
5956 = 14² + 24² + 72² is the sum of 3 positive squares.
5956² = 2756² + 5280² is the sum of 2 positive squares in 1 way.
5956² is the sum of 3 positive squares.
5956 is a proper divisor of 1973⁶ - 1.
5956 = '595' + '6' is the concatenation of 2 triangular numbers.
5956 is palindromic in (at least) the following bases: 21, and -34.
5956 in base 19 = g99 and consists of only the digits '9' and 'g'.
5956 in base 21 = dad and consists of only the digits 'a' and 'd'.
5956 in base 31 = 664 and consists of only the digits '4' and '6'.
5956 in base 34 = 556 and consists of only the digits '5' and '6'.
5956 in base 38 = 44S and consists of only the digits '4' and 'S'.
5956 in base 44 = 33G and consists of only the digits '3' and 'G'.
5956 in base 54 = 22G and consists of only the digits '2' and 'G'.

The number 5956 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005541: Numbers n such that 8*3^n - 1 is prime.
A138989: a(n) = Frobenius number for 3 successive primes = F[p(n),p(n+1),p(n+2)].
A160792: Vertex number of a rectangular spiral related to prime numbers. The distances between nearest edges of the spiral that are parallel to the initial edge are the prime numbers, while the distances between nearest edges perpendicular to the initial edge are all one.
A169912: Number of irreducible Boolean polynomials of degree n.
A177915: Numbers n such that n^3 divides 15^(n^2)-1.
A204301: T(n,k)=Number of nXk 0..3 arrays with every element neighboring horizontally or vertically both a 0 and a 1, and 2 introduced before 3 in row major order
A227914: Length of longest chain of nonempty proper subsemigroups of the symmetric inverse monoid.
A235332: a(n) = n*(9*n + 25)/2 + 6.
A271293: Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 345", based on the 5-celled von Neumann neighborhood.
A295952: Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n), where a(0) = 1, a(1) = 5, b(0) = 2, b(1) = 3, b(2) = 4, and (a(n)) and (b(n)) are increasing complementary sequences.

Number of the day: 184904

Properties of the number 184904:

184904 = 2³ × 29 × 797 is the 168166^th composite number and is not squarefree.
184904 has 3 distinct prime factors, 16 divisors, 7 antidivisors and 89152 totatives.
184904 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 184904 results in a semiprime.
184904 = 37² + … + 84² is the sum of at least 2 consecutive positive squares in 1 way.
184904 = 3³ + 21³ + 56³ is the sum of 3 positive cubes in 1 way.
184904 = 46227² - 46225² = 23115² - 23111² = 1623² - 1565² = 855² - 739² is the difference of 2 nonnegative squares in 4 ways.
184904 is the difference of 2 positive pentagonal numbers in 1 way.
184904 = 298² + 310² = 2² + 430² is the sum of 2 positive squares in 2 ways.
184904 = 8² + 58² + 426² is the sum of 3 positive squares.
184904² = 127520² + 133896² = 1720² + 184896² = 7296² + 184760² = 128760² + 132704² is the sum of 2 positive squares in 4 ways.
184904² is the sum of 3 positive squares.
184904 is a proper divisor of 233³⁹⁸ - 1.
184904 is palindromic in (at least) base -65.

Number of the day: 52760

Properties of the number 52760:

52760 = 2³ × 5 × 1319 is the 47373^th composite number and is not squarefree.
52760 has 3 distinct prime factors, 16 divisors, 11 antidivisors and 21088 totatives.
52760 has an oblong digit sum 20 in base 10.
52760 = 13191² - 13189² = 6597² - 6593² = 2643² - 2633² = 1329² - 1309² is the difference of 2 nonnegative squares in 4 ways.
52760 is the difference of 2 positive pentagonal numbers in 2 ways.
52760 = 28² + 30² + 226² is the sum of 3 positive squares.
52760² = 31656² + 42208² is the sum of 2 positive squares in 1 way.
52760² is the sum of 3 positive squares.
52760 is a proper divisor of 281⁶⁵⁹ - 1.
52760 is palindromic in (at least) base -84.

The number 52760 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A070893: Let r, s, t be three permutations of the set {1,2,3,..,n}; a(n)= value of sum_{i=1..n} r(i)*s(i)*t(i), with r={1,2,3,..,n}; s={n,n-1,..,1} and t={n,n-2,n-4,...,1,...,n-3,n-1}.
A231732: Triangular array read by rows: row n shows the coefficients of the polynomial u(n) = c(0) + c(1)*x + ... + c(n)*x^(n) which is the numerator of the n-th convergent of the continued fraction [k, k, k, ... ], where k = (x + 2)/(x + 1).
A264390: Partial sums of A267326.

Number of the day: 841808

Properties of the number 841808:

841808 = 2⁴ × 11 × 4783 is the 774790^th composite number and is not squarefree.
841808 has 3 distinct prime factors, 20 divisors, 11 antidivisors and 382560 totatives.
841808 has a prime digit sum 29 in base 10.
841808 = 210453² - 210451² = 105228² - 105224² = 52617² - 52609² = 19143² - 19121² = 9588² - 9544² = 4827² - 4739² is the difference of 2 nonnegative squares in 6 ways.
841808 is the sum of 2 positive triangular numbers.
841808 is the difference of 2 positive pentagonal numbers in 2 ways.
841808 = 24² + 196² + 896² is the sum of 3 positive squares.
841808² is the sum of 3 positive squares.
841808 is a proper divisor of 353⁷⁹⁷ - 1.

Number of the day: 268844

Properties of the number 268844:

268844 = 2² × 67211 is the 245293^th composite number and is not squarefree.
268844 has 2 distinct prime factors, 6 divisors, 7 antidivisors and 134420 totatives.
268844 = 67212² - 67210² is the difference of 2 nonnegative squares in 1 way.
268844 is the difference of 2 positive pentagonal numbers in 1 way.
268844 = 62² + 70² + 510² is the sum of 3 positive squares.
268844² is the sum of 3 positive squares.
268844 is a proper divisor of 757⁴⁷⁰ - 1.

Number of the day: 59178

Properties of the number 59178:

59178 = 2 × 3 × 7 × 1409 is the 53194^th composite number and is squarefree.
59178 has 4 distinct prime factors, 16 divisors, 11 antidivisors and 16896 totatives.
59178 has a sphenic digit sum 30 in base 10.
59178 has an oblong digit sum 30 in base 10.
Reversing the decimal digits of 59178 results in a sphenic number.
59178 is the sum of 2 positive triangular numbers.
59178 is the difference of 2 positive pentagonal numbers in 4 ways.
59178 = 16² + 29² + 241² is the sum of 3 positive squares.
59178² = 6678² + 58800² is the sum of 2 positive squares in 1 way.
59178² is the sum of 3 positive squares.
59178 is a proper divisor of 1861⁴ - 1.
59178 is palindromic in (at least) base -58.
59178 in base 20 = 77ii and consists of only the digits '7' and 'i'.
59178 in base 57 = ICC and consists of only the digits 'C' and 'I'.

The number 59178 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A210167: Number of (n+1)X2 0..3 arrays containing all values 0..3 with every 2X2 subblock having two or four distinct values, and new values 0..3 introduced in row major order
A210172: Number of (n+1)X7 0..3 arrays containing all values 0..3 with every 2X2 subblock having two or four distinct values, and new values 0..3 introduced in row major order
A210174: T(n,k)=Number of (n+1)X(k+1) 0..3 arrays containing all values 0..3 with every 2X2 subblock having two or four distinct values, and new values 0..3 introduced in row major order
A286560: Compound filter (summands of A004001 & summands of A005185): a(n) = P(A286541(n), A286559(n)), where P(n,k) is sequence A000027 used as a pairing function, with a(1) = a(2) = 0.
A294609: Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} 1/(1-j*x^j)^(j^(k*j)) in powers of x.
A294950: Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} 1/(1-j^(k*j)*x^j)^j in powers of x.

Number of the day: 66964

Paul Cohen was born on this day 84 years ago.

Properties of the number 66964:

66964 = 2² × 16741 is the 60290^th composite number and is not squarefree.
66964 has 2 distinct prime factors, 6 divisors, 13 antidivisors and 33480 totatives.
66964 has an emirp digit sum 31 in base 10.
Reversing the decimal digits of 66964 results in a sphenic number.
66964 = 16742² - 16740² is the difference of 2 nonnegative squares in 1 way.
66964 is the sum of 2 positive triangular numbers.
66964 is the difference of 2 positive pentagonal numbers in 1 way.
66964 = 20² + 258² is the sum of 2 positive squares in 1 way.
66964 = 30² + 92² + 240² is the sum of 3 positive squares.
66964² = 10320² + 66164² is the sum of 2 positive squares in 1 way.
66964² is the sum of 3 positive squares.
66964 is a proper divisor of 1381³¹ - 1.
66964 is palindromic in (at least) base -39.
66964 in base 39 = 1511 and consists of only the digits '1' and '5'.

The number 66964 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A066487: a(n) = min( x : x^4 + n^4 = 0 mod (x+n-1) ).
A270906: Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by "Rule 214", based on the 5-celled von Neumann neighborhood.

Number of the day: 1150

Sophie Germain was born on this day 242 years ago.

Alexander Craig Aitken was born on this day 123 years ago.

Properties of the number 1150:

1150 = 2 × 5² × 23 is the 960^th composite number and is not squarefree.
1150 has 3 distinct prime factors, 12 divisors, 15 antidivisors and 440 totatives.
1150 has a prime digit sum 7 in base 10.
1150 is the difference of 2 positive pentagonal numbers in 3 ways.
1150 = 5² + 6² + 33² is the sum of 3 positive squares.
1150² = 690² + 920² = 322² + 1104² is the sum of 2 positive squares in 2 ways.
1150² is the sum of 3 positive squares.
1150 is a proper divisor of 599² - 1.
1150 is palindromic in (at least) the following bases: 13, 45, 49, and -28.
1150 in base 7 = 3232 and consists of only the digits '2' and '3'.
1150 in base 13 = 6a6 and consists of only the digits '6' and 'a'.
1150 in base 19 = 33a and consists of only the digits '3' and 'a'.
1150 in base 33 = 11s and consists of only the digits '1' and 's'.

The number 1150 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A052221: Numbers whose sum of digits is 7.
A054000: a(n) = 2*n^2 - 2.
A084646: Hypotenuses for which there exist exactly 2 distinct integer triangles.
A096173: Numbers k such that k^3+1 is an odd semiprime.
A126075: Triangle T(n,k), 0 <= k <= n, read by rows, defined by: T(0,0)=1, T(n,k)=0 if k < 0 or if k > n, T(n,0) = 2*T(n-1,0) + T(n-1,1), T(n,k) = T(n-1,k-1) + T(n-1,k+1) for k >= 1.
A213709: Number of steps to go from 2^(n+1)-1 to (2^n)-1 using the iterative process described in A071542.
A256631: Numbers n such that the decimal expansions of both n and n^2 have 0 as smallest digit and 5 as largest digit.
A299263: Partial sums of A299257.
A299277: Coordination sequence for "pcu-i" 3D uniform tiling.
A299279: Coordination sequence for "reo" 3D uniform tiling.