Number of the day: 963994

Properties of the number 963994:

963994 = 2 × 481997 is semiprime and squarefree.
963994 has 2 distinct prime factors, 4 divisors, 37 antidivisors and 481996 totatives.
Reversing the decimal digits of 963994 results in a sphenic number.
963994 is the sum of 2 positive triangular numbers.
963994 is the difference of 2 positive pentagonal numbers in 2 ways.
963994 = 675² + 713² is the sum of 2 positive squares in 1 way.
963994 = 93² + 128² + 969² is the sum of 3 positive squares.
963994² = 52744² + 962550² is the sum of 2 positive squares in 1 way.
963994² is the sum of 3 positive squares.
963994 is a proper divisor of 23²⁹³⁹ - 1.
963994 is an emirpimes in (at least) the following bases: 5, 19, 23, 24, 28, 29, 31, 32, 41, 43, 57, 73, 74, 75, 78, 87, 88, 90, 93, and 94.

Number of the day: 43292

Properties of the number 43292:

43292 = 2² × 79 × 137 is the 38773^th composite number and is not squarefree.
43292 has 3 distinct prime factors, 12 divisors, 27 antidivisors and 21216 totatives.
43292 has an oblong digit sum 20 in base 10.
Reversing the decimal digits of 43292 results in a sphenic number.
43292 = 10824² - 10822² = 216² - 58² is the difference of 2 nonnegative squares in 2 ways.
43292 is the difference of 2 positive pentagonal numbers in 2 ways.
43292 is not the sum of 3 positive squares.
43292² = 27808² + 33180² is the sum of 2 positive squares in 1 way.
43292² is the sum of 3 positive squares.
43292 is a proper divisor of 823²⁶ - 1.
43292 is palindromic in (at least) the following bases: -63, and -67.
43292 in base 24 = 333k and consists of only the digits '3' and 'k'.
43292 in base 62 = BGG and consists of only the digits 'B' and 'G'.

Number of the day: 351

Properties of the number 351:

351 = 3³ × 13 is the 280^th composite number and is not squarefree.
351 has 2 distinct prime factors, 8 divisors, 9 antidivisors and 216 totatives.
351 has a semiprime digit sum 9 in base 10.
351 has an emirpimes digit product 15 in base 10.
351 has a triangular digit product 15 in base 10.
Reversing the decimal digits of 351 results in a triangular number.
351 = 7³ + 2³ is the sum of 2 positive cubes in 1 way.
351 = 176² - 175² = 60² - 57² = 24² - 15² = 20² - 7² is the difference of 2 nonnegative squares in 4 ways.
351 = (26 × 27)/2 is a triangular number.
351 is not the sum of 3 positive squares.
351² = 135² + 324² is the sum of 2 positive squares in 1 way.
351² is the sum of 3 positive squares.
351 is a proper divisor of 53² - 1.
351 = '35' + '1' is the concatenation of 2 pentagonal numbers.
351 is palindromic in (at least) the following bases: 14, 26, 38, -7, -12, -25, -35, -50, and -70.
351 in base 3 = 111000 and consists of only the digits '0' and '1'.
351 in base 4 = 11133 and consists of only the digits '1' and '3'.
351 in base 7 = 1011 and consists of only the digits '0' and '1'.
351 in base 14 = 1b1 and consists of only the digits '1' and 'b'.
351 in base 18 = 119 and consists of only the digits '1' and '9'.

The number 351 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000217: Triangular numbers: a(n) = binomial(n+1,2) = n(n+1)/2 = 0 + 1 + 2 + ... + n.
A000931: Padovan sequence (or Padovan numbers): a(n) = a(n-2) + a(n-3) with a(0)=1, a(1)=a(2)=0.
A003325: Numbers that are the sum of 2 positive cubes.
A005251: a(0) = 0, a(1) = a(2) = a(3) = 1; thereafter, a(n) = a(n-1) + a(n-2) + a(n-4).
A005836: Numbers n whose base 3 representation contains no 2.
A014105: Second hexagonal numbers: a(n) = n*(2n+1).
A014580: Binary irreducible polynomials (primes in the ring GF(2)[X]), evaluated at X=2.
A014613: Numbers that are products of 4 primes (these numbers are sometimes called "4-almost primes", a generalization of semiprimes).
A074377: Generalized 10-gonal numbers: n*(4*n-3), n=0, +- 1, +- 2, +- 3,...
A084438: Positive integers n such that n!!!-1 = A007661(n)-1 is prime.

Number of the day: 5001

Properties of the number 5001:

5001 is a cyclic number.
5001 = 3 × 1667 is semiprime and squarefree.
5001 has 2 distinct prime factors, 4 divisors, 7 antidivisors and 3332 totatives.
5001 has a semiprime digit sum 6 in base 10.
5001 has a triangular digit sum 6 in base 10.
5001 has an oblong digit sum 6 in base 10.
Reversing the decimal digits of 5001 results in a sphenic number.
5001 = (14 × 15)/2 + … + (31 × 32)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
5001 = 2501² - 2500² = 835² - 832² is the difference of 2 nonnegative squares in 2 ways.
5001 is the sum of 2 positive triangular numbers.
5001 is the difference of 2 positive pentagonal numbers in 1 way.
5001 = 1² + 10² + 70² is the sum of 3 positive squares.
5001² is the sum of 3 positive squares.
5001 is a proper divisor of 877¹⁷ - 1.
5001 is an emirpimes in (at least) the following bases: 7, 11, 14, 19, 25, 29, 30, 38, 40, 43, 45, 49, 51, 54, 55, 57, 60, 61, 66, 67, 68, 71, 75, 76, 78, 79, 83, 84, 87, 89, 90, 91, 93, 94, and 95.
5001 is palindromic in (at least) the following bases: 6, 8, 18, 27, -23, -24, -42, -49, and -100.
5001 in base 8 = 11611 and consists of only the digits '1' and '6'.
5001 in base 9 = 6766 and consists of only the digits '6' and '7'.
5001 in base 18 = f7f and consists of only the digits '7' and 'f'.
5001 in base 22 = a77 and consists of only the digits '7' and 'a'.
5001 in base 23 = 9aa and consists of only the digits '9' and 'a'.
5001 in base 27 = 6n6 and consists of only the digits '6' and 'n'.

The number 5001 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A033819: Trimorphic numbers: n^3 ends with n. Also m-morphic numbers for all m>5 such that m-1 is not divisible by 10 and m==3 (mod 4).
A069860: Numbers n that divide the concatenation of n+1 and n+2.
A081585: Third row of Pascal-(1,3,1) array A081578.
A105476: Number of compositions of n when each even part can be of two kinds.
A136811: Numbers n such that n and the square of n use only the digits 0, 1, 2, 3 and 5.
A144390: a(n) = 3*n^2 - n - 1.
A216899: Smallest palindromic number of 5 digits in two bases differing by n.
A255830: Numbers D such that D^2 = A^4 + B^5 + C^6 for some positive integers A, B, C.
A256631: Numbers n such that the decimal expansions of both n and n^2 have 0 as smallest digit and 5 as largest digit.
A259384: Palindromic numbers in bases 6 and 8 written in base 10.

Number of the day: 7215662483

Giuseppe Peano was born on this day 159 years ago.

Properties of the number 7215662483:

7215662483 is a cyclic number.
7215662483 = 131 × 55081393 is semiprime and squarefree.
7215662483 has 2 distinct prime factors, 4 divisors, 9 antidivisors and 7160580960 totatives.
Reversing the decimal digits of 7215662483 results in a sphenic number.
7215662483 = 815³ + 1093³ + 1751³ is the sum of 3 positive cubes in 1 way.
7215662483 = 3607831242² - 3607831241² = 27540762² - 27540631² is the difference of 2 nonnegative squares in 2 ways.
7215662483 is the difference of 2 positive pentagonal numbers in 2 ways.
7215662483 = 7² + 97² + 84945² is the sum of 3 positive squares.
7215662483² = 3173216275² + 6480469392² is the sum of 2 positive squares in 1 way.
7215662483² is the sum of 3 positive squares.
7215662483 is a proper divisor of 541^5158920 - 1.
7215662483 is an emirpimes in (at least) the following bases: 2, 3, 8, 11, 12, 13, 16, 17, 18, 19, 21, 24, 25, 29, 30, 33, 35, 43, 44, 47, 50, 52, 54, 57, 59, 60, 62, 65, 66, 69, 74, 82, 84, 90, 92, and 95.

Number of the day: 4803

Properties of the number 4803:

4803 is a cyclic number.
4803 = 3 × 1601 is semiprime and squarefree.
4803 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 3200 totatives.
4803 has an emirpimes digit sum 15 in base 10.
4803 has a triangular digit sum 15 in base 10.
4803 = 2402² - 2401² = 802² - 799² is the difference of 2 nonnegative squares in 2 ways.
4803 is the sum of 2 positive triangular numbers.
4803 is the difference of 2 positive pentagonal numbers in 1 way.
4803 = 5² + 17² + 67² is the sum of 3 positive squares.
4803² = 240² + 4797² is the sum of 2 positive squares in 1 way.
4803² is the sum of 3 positive squares.
4803 is a proper divisor of 163⁵ - 1.
4803 = '4' + '803' is the concatenation of 2 semiprime numbers.
4803 is an emirpimes in (at least) the following bases: 2, 15, 17, 21, 22, 23, 25, 30, 31, 33, 36, 37, 39, 56, 60, 63, 69, 73, 75, 76, 83, 84, 85, 86, 93, and 99.
4803 is palindromic in (at least) the following bases: 40, -18, -40, -48, and -98.
4803 in base 18 = eef and consists of only the digits 'e' and 'f'.
4803 in base 24 = 883 and consists of only the digits '3' and '8'.
4803 in base 39 = 366 and consists of only the digits '3' and '6'.
4803 in base 40 = 303 and consists of only the digits '0' and '3'.

The number 4803 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A050797: Numbers n such that n^2 - 1 is expressible as the sum of two nonzero squares in exactly one way.
A095066: Number of fib001 primes (A095086) in range ]2^n,2^(n+1)].
A105632: Triangle, read by rows, where the g.f. A(x,y) satisfies the equation: A(x,y) = 1/(1-x*y) + x*A(x,y) + x^2*A(x,y)^2.
A120041: Number of 10-almost primes k such that 2^n < k <= 2^(n+1).
A160422: Number of "ON" cells at n-th stage in simple 2-dimensional cellular automaton whose virtual skeleton is a polyedge as the toothpick structure of A139250 but with toothpicks of length 6.
A182714: Number of 4's in the last section of the set of partitions of n.
A188536: Potential magic constants of 7 X 7 magic squares composed of consecutive primes.
A206920: Sum of the first n binary palindromes; a(n) = sum(k=1..n, A006995(k)).
A260052: Composites whose prime factorization in base 8 is an anagram of the number in base 8.
A261780: Number A(n,k) of compositions of n where each part i is marked with a word of length i over a k-ary alphabet whose letters appear in alphabetical order; square array A(n,k), n>=0, k>=0, read by antidiagonals.

Number of the day: 45489434

Properties of the number 45489434:

45489434 = 2 × 22744717 is semiprime and squarefree.
45489434 has 2 distinct prime factors, 4 divisors, 13 antidivisors and 22744716 totatives.
45489434 has a prime digit sum 41 in base 10.
45489434 has sum of divisors equal to 68234154 which is a sphenic number.
Reversing the decimal digits of 45489434 results in a sphenic number.
45489434 = 2975² + 6053² is the sum of 2 positive squares in 1 way.
45489434 = 137² + 172² + 6741² is the sum of 3 positive squares.
45489434² = 27788184² + 36015350² is the sum of 2 positive squares in 1 way.
45489434² is the sum of 3 positive squares.
45489434 is a proper divisor of 7^1895393 - 1.
45489434 = '4548943' + '4' is the concatenation of 2 semiprime numbers.
45489434 = '45489' + '434' is the concatenation of 2 sphenic numbers.
45489434 is an emirpimes in (at least) the following bases: 7, 9, 11, 23, 62, 66, 67, 70, 72, 74, 77, 80, 86, 91, 93, 96, and 99.

Number of the day: 2594

Properties of the number 2594:

2594 = 2 × 1297 is semiprime and squarefree.
2594 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 1296 totatives.
2594 has an oblong digit sum 20 in base 10.
2594 = (34 × 35)/2 + … + (37 × 38)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
2594 is the sum of 2 positive triangular numbers.
2594 = 35² + 37² is the sum of 2 positive squares in 1 way.
2594 = 7² + 12² + 49² is the sum of 3 positive squares.
2594² = 144² + 2590² is the sum of 2 positive squares in 1 way.
2594² is the sum of 3 positive squares.
2594 is a proper divisor of 1663⁶ - 1.
2594 = '25' + '94' is the concatenation of 2 semiprime numbers.
2594 is an emirpimes in (at least) the following bases: 4, 8, 11, 16, 21, 23, 26, 28, 30, 35, 39, 41, 43, 45, 46, 48, 55, 61, 62, 63, 67, 68, 69, 71, 75, 76, 81, 82, 83, 86, 89, 96, and 98.
2594 is palindromic in (at least) the following bases: 6, 32, 36, -6, -36, and -48.
2594 in base 4 = 220202 and consists of only the digits '0' and '2'.
2594 in base 6 = 20002 and consists of only the digits '0' and '2'.
2594 in base 16 = a22 and consists of only the digits '2' and 'a'.
2594 in base 31 = 2ll and consists of only the digits '2' and 'l'.
2594 in base 32 = 2h2 and consists of only the digits '2' and 'h'.
2594 in base 35 = 244 and consists of only the digits '2' and '4'.
2594 in base 36 = 202 and consists of only the digits '0' and '2'.
2594 in base 50 = 11i and consists of only the digits '1' and 'i'.

The number 2594 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005893: Number of points on surface of tetrahedron: 2n^2 + 2 (coordination sequence for sodalite net) for n>0.
A051989: Discriminants of real quadratic fields with class number 2 and related continued fraction period length of 24.
A077068: Semiprimes of form prime + 1.
A078164: Numbers n such that phi(n) is a perfect biquadrate.
A092228: Numbers n such that numerator of Bernoulli(2n) is divisible by 233, the ninth irregular prime.
A126171: Number of infinitary amicable pairs (i,j) with i<j and i<=10^n.
A135110: Positive numbers such that the digital sum base 2 and the digital sum base 10 are in a ratio of 2:10.
A207815: Triangle of coefficients of Chebyshev's S(n,x-3) polynomials (exponents of x in increasing order).
A218897: T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal, diagonal or antidiagonal neighbors in a random 0..1 nXk array
A231515: T(n,k)=Number of nXk 0..1 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors

Number of the day: 73464

Properties of the number 73464:

73464 = 2³ × 3 × 3061 is the 66209^th composite number and is not squarefree.
73464 has 3 distinct prime factors, 16 divisors, 15 antidivisors and 24480 totatives.
73464 has a triangular digit product 2016 in base 10.
Reversing the decimal digits of 73464 results in a sphenic number.
73464 = 18367² - 18365² = 9185² - 9181² = 6125² - 6119² = 3067² - 3055² is the difference of 2 nonnegative squares in 4 ways.
73464 is the sum of 2 positive triangular numbers.
73464 = 2² + 52² + 266² is the sum of 3 positive squares.
73464² = 15840² + 71736² is the sum of 2 positive squares in 1 way.
73464² is the sum of 3 positive squares.
73464 is a proper divisor of 1867³⁰ - 1.
73464 = '7346' + '4' is the concatenation of 2 semiprime numbers.
73464 is palindromic in (at least) base -61.
73464 in base 56 = NNm and consists of only the digits 'N' and 'm'.
73464 in base 60 = KOO and consists of only the digits 'K' and 'O'.

Number of the day: 3974

Properties of the number 3974:

3974 = 2 × 1987 is semiprime and squarefree.
3974 has 2 distinct prime factors, 4 divisors, 5 antidivisors and 1986 totatives.
3974 has a prime digit sum 23 in base 10.
3974 has an oblong digit product 756 in base 10.
Reversing the decimal digits of 3974 results in a prime.
3974 = 30² + … + 33² is the sum of at least 2 consecutive positive squares in 1 way.
3974 = 1² + 2² + 63² is the sum of 3 positive squares.
3974² is the sum of 3 positive squares.
3974 is a proper divisor of 647³ - 1.
3974 = '39' + '74' is the concatenation of 2 semiprime numbers.
3974 is an emirpimes in (at least) the following bases: 5, 6, 8, 12, 13, 16, 19, 20, 25, 26, 28, 29, 35, 36, 38, 39, 42, 44, 47, 48, 54, 56, 57, 59, 60, 63, 64, 67, 68, 71, 74, 75, 80, 81, 84, 86, 91, and 100.
3974 is palindromic in (at least) the following bases: 17, and 27.
3974 in base 17 = dcd and consists of only the digits 'c' and 'd'.
3974 in base 26 = 5mm and consists of only the digits '5' and 'm'.
3974 in base 27 = 5c5 and consists of only the digits '5' and 'c'.
3974 in base 31 = 446 and consists of only the digits '4' and '6'.
3974 in base 44 = 22E and consists of only the digits '2' and 'E'.

The number 3974 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A007684: Prime(n)*...*prime(a(n)) is the least product of consecutive primes that is non-deficient.
A007707: Prime(n)*...*prime(a(n)) is the least product of consecutive primes which is abundant.
A027575: a(n) = n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2.
A059886: a(n) = |{m : multiplicative order of 4 mod m=n}|.
A068336: a(1) = 1; a(n+1) = 1 + sum{k|n} a(k), sum is over the positive divisors, k, of n.
A081268: Diagonal of triangular spiral in A051682.
A104577: Indices of prime generalized tetranacci numbers, A073817.
A191455: Dispersion of (floor(n*e)), by antidiagonals.
A218064: T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..1 nXk array
A227743: Integers n for which A173318(n) is a square.

Number of the day: 918776

Augustin-Louis Cauchy was born on this day 228 years ago.

Properties of the number 918776:

918776 = 2³ × 114847 is the 846129^th composite number and is not squarefree.
918776 has 2 distinct prime factors, 8 divisors, 9 antidivisors and 459384 totatives.
918776 has a semiprime digit sum 38 in base 10.
Reversing the decimal digits of 918776 results in a semiprime.
918776 = 229695² - 229693² = 114849² - 114845² is the difference of 2 nonnegative squares in 2 ways.
918776 = 116² + 134² + 942² is the sum of 3 positive squares.
918776² is the sum of 3 positive squares.
918776 is a proper divisor of 73¹⁹¹⁴¹ - 1.
918776 = '91877' + '6' is the concatenation of 2 semiprime numbers.

Number of the day: 43040741

Properties of the number 43040741:

43040741 is a cyclic number.
43040741 = 31 × 1388411 is semiprime and squarefree.
43040741 has 2 distinct prime factors, 4 divisors, 23 antidivisors and 41652300 totatives.
43040741 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 43040741 results in an emirpimes.
43040741 = 21520371² - 21520370² = 694221² - 694190² is the difference of 2 nonnegative squares in 2 ways.
43040741 is the difference of 2 positive pentagonal numbers in 2 ways.
43040741 = 49² + 176² + 6558² is the sum of 3 positive squares.
43040741² is the sum of 3 positive squares.
43040741 is a proper divisor of 557²⁷⁷⁶⁸² - 1.
43040741 is an emirpimes in (at least) the following bases: 6, 8, 9, 10, 11, 13, 16, 19, 21, 23, 27, 28, 31, 37, 41, 42, 47, 49, 53, 55, 58, 62, 69, 70, 71, 73, 75, 77, 78, 81, 86, 89, 90, 93, and 98.

Number of the day: 61618

Properties of the number 61618:

61618 = 2 × 30809 is semiprime and squarefree.
61618 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 30808 totatives.
61618 has a semiprime digit sum 22 in base 10.
61618 is the sum of 2 positive triangular numbers.
61618 is the difference of 2 positive pentagonal numbers in 2 ways.
61618 = 137² + 207² is the sum of 2 positive squares in 1 way.
61618 = 43² + 60² + 237² is the sum of 3 positive squares.
61618² = 24080² + 56718² is the sum of 2 positive squares in 1 way.
61618² is the sum of 3 positive squares.
61618 is a proper divisor of 7³⁸⁵¹ - 1.
61618 = '6' + '1618' is the concatenation of 2 semiprime numbers.
61618 is an emirpimes in (at least) the following bases: 4, 6, 9, 11, 13, 16, 22, 23, 25, 32, 35, 37, 44, 54, 56, 59, 60, 68, 73, 74, 76, 77, 88, 89, 97, and 100.
61618 is palindromic in (at least) the following bases: 41, and 49.
61618 in base 7 = 344434 and consists of only the digits '3' and '4'.
61618 in base 41 = aQa and consists of only the digits 'Q' and 'a'.
61618 in base 49 = PWP and consists of only the digits 'P' and 'W'.
61618 in base 55 = KKI and consists of only the digits 'I' and 'K'.
61618 in base 58 = IIM and consists of only the digits 'I' and 'M'.

The number 61618 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A187858: Number of 3-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-queen's tours (antidiagonal moves become knight moves) on an n X n board summed over all starting positions

Number of the day: 4603

Properties of the number 4603:

4603 is a cyclic number.
4603 is the 623^th prime.
4603 has 21 antidivisors and 4602 totatives.
4603 has an emirp digit sum 13 in base 10.
4603 has a Fibonacci digit sum 13 in base 10.
4603 = 2302² - 2301² is the difference of 2 nonnegative squares in 1 way.
4603 is the sum of 2 positive triangular numbers.
4603 is the difference of 2 positive pentagonal numbers in 1 way.
4603 = 3² + 25² + 63² is the sum of 3 positive squares.
4603² is the sum of 3 positive squares.
4603 is a proper divisor of 179³ - 1.
4603 is an emirp in (at least) the following bases: 4, 13, 17, 19, 22, 24, 29, 33, 35, 37, 38, 49, 50, 51, 55, 65, 67, 71, 75, 77, 78, 81, 83, 86, 93, 95, and 96.
4603 is palindromic in (at least) the following bases: 43, 59, -40, -46, and -78.
4603 in base 17 = ffd and consists of only the digits 'd' and 'f'.
4603 in base 39 = 311 and consists of only the digits '1' and '3'.
4603 in base 42 = 2PP and consists of only the digits '2' and 'P'.
4603 in base 43 = 2L2 and consists of only the digits '2' and 'L'.
4603 in base 58 = 1LL and consists of only the digits '1' and 'L'.
4603 in base 59 = 1J1 and consists of only the digits '1' and 'J'.

The number 4603 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A031936: Lower prime of a difference of 18 between consecutive primes.
A056108: Fourth spoke of a hexagonal spiral.
A066540: The first of two consecutive primes with equal digital sums.
A095673: Primes p = p_(n+1) such that p_n + p_(n+2) = 2*p_(n+1) + 12.
A100201: Primes of the form 23n+3.
A104824: Primes from merging of 4 successive digits in decimal expansion of Pi.
A113743: Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 6 multiples of n-1, n-2, ..., 1.
A198164: Primes from merging of 4 successive digits in decimal expansion of sqrt(2).
A272160: Primes of the form abs(8n^2 - 488n + 7243) in order of increasing nonnegative values of n.
A275183: T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,0) or (-1,1) and new values introduced in order 0..2.

Number of the day: 412485

Pierre de Fermat was born on this day 416 years ago.

Properties of the number 412485:

412485 is a cyclic number.
412485 = 3 × 5 × 107 × 257 is the 377675^th composite number and is squarefree.
412485 has 4 distinct prime factors, 16 divisors, 23 antidivisors and 217088 totatives.
Reversing the decimal digits of 412485 results in a sphenic number.
412485 = 206243² - 206242² = 68749² - 68746² = 41251² - 41246² = 13757² - 13742² = 1981² - 1874² = 931² - 674² = 803² - 482² = 653² - 118² is the difference of 2 nonnegative squares in 8 ways.
412485 is the difference of 2 positive pentagonal numbers in 3 ways.
412485 = 20² + 71² + 638² is the sum of 3 positive squares.
412485² = 204477² + 358236² = 51360² + 409275² = 286653² + 296604² = 247491² + 329988² is the sum of 2 positive squares in 4 ways.
412485² is the sum of 3 positive squares.
412485 is a proper divisor of 643¹⁶ - 1.
412485 is palindromic in (at least) base -92.

Number of the day: 229585

Arthur Cayley was born on this day 196 years ago.

Properties of the number 229585:

229585 is a cyclic number.
229585 = 5 × 17 × 37 × 73 is the 209187^th composite number and is squarefree.
229585 has 4 distinct prime factors, 16 divisors, 25 antidivisors and 165888 totatives.
229585 has an emirp digit sum 31 in base 10.
229585 = 114793² - 114792² = 22961² - 22956² = 6761² - 6744² = 3121² - 3084² = 1609² - 1536² = 1393² - 1308² = 713² - 528² = 497² - 132² is the difference of 2 nonnegative squares in 8 ways.
229585 is the sum of 2 positive triangular numbers.
229585 is the difference of 2 positive pentagonal numbers in 7 ways.
229585 = 297² + 376² = 159² + 452² = 236² + 417² = 88² + 471² = 324² + 353² = 192² + 439² = 144² + 457² = 12² + 479² is the sum of 2 positive squares in 8 ways.
229585 = 3² + 70² + 474² is the sum of 3 positive squares.
229585² = 156585² + 167900² = 108040² + 202575² = 36500² + 226665² = 146775² + 176540² = 81585² + 214600² = 7575² + 229460² = 121540² + 194775² = 51800² + 223665² = 23540² + 228375² = 147852² + 175639² = 118193² + 196824² = 82896² + 214097² = 106799² + 203232² = 35113² + 226884² = 40369² + 226008² = 143736² + 179023² = 122729² + 194028² = 53167² + 223344² = 159432² + 165199² = 97236² + 207977² = 24528² + 228271² = 155857² + 168576² = 92759² + 210012² = 19633² + 228744² = 131616² + 188113² = 63492² + 220631² = 11496² + 229297² = 137751² + 183668² = 129064² + 189873² = 70737² + 218416² = 118048² + 196911² = 47804² + 224553² = 27608² + 227919² = 90321² + 211072² = 16983² + 228956² = 58191² + 222088² = 150960² + 172975² = 114665² + 198900² = 86700² + 212585² = 74460² + 217175² is the sum of 2 positive squares in 40 ways.
229585² is the sum of 3 positive squares.
229585 is a proper divisor of 1511⁸ - 1.

The number 229585 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A218135: Norm of coefficients in the expansion of 1 / (1 - x - 2*I*x^2), where I^2=-1.
A255214: Number of partitions of n^2 into at most 10 square parts.

Number of the day: 719628

Happy Pythagorean Theorem Day!

Properties of the number 719628:

719628 = 2² × 3 × 7 × 13 × 659 is the 661629^th composite number and is not squarefree.
719628 has 5 distinct prime factors, 48 divisors, 19 antidivisors and 189504 totatives.
719628 has a semiprime digit sum 33 in base 10.
719628 = 179908² - 179906² = 59972² - 59966² = 25708² - 25694² = 13852² - 13826² = 8588² - 8546² = 4652² - 4574² = 2068² - 1886² = 932² - 386² is the difference of 2 nonnegative squares in 8 ways.
719628 is the difference of 2 positive pentagonal numbers in 3 ways.
719628 = 106² + 214² + 814² is the sum of 3 positive squares.
719628² = 276780² + 664272² is the sum of 2 positive squares in 1 way.
719628² is the sum of 3 positive squares.
719628 is a proper divisor of 1319¹² - 1.

The number 719628 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A241576: Third differences of A001521.
A244020: Number of new points at the n-th step of the following iteration, starting with four points in general position in the real projective plane: dualize the current pointset to a family of lines, take all intersections of those lines, repeat.

Number of the day: 749736

Properties of the number 749736:

749736 = 2³ × 3⁴ × 13 × 89 is the 689518^th composite number and is not squarefree.
749736 has 4 distinct prime factors, 80 divisors, 21 antidivisors and 228096 totatives.
749736 has a triangular digit sum 36 in base 10.
749736 is the difference of 2 nonnegative squares in 20 ways.
749736 is the sum of 2 positive triangular numbers.
749736 is the difference of 2 positive pentagonal numbers in 1 way.
749736 = 594² + 630² = 306² + 810² is the sum of 2 positive squares in 2 ways.
749736 = 56² + 194² + 842² is the sum of 3 positive squares.
749736² = 328536² + 673920² = 44064² + 748440² = 495720² + 562464² = 288360² + 692064² is the sum of 2 positive squares in 4 ways.
749736² is the sum of 3 positive squares.
749736 is a proper divisor of 179¹⁸ - 1.
749736 in base 34 = j2j2 and consists of only the digits '2' and 'j'.
749736 in base 35 = hh11 and consists of only the digits '1' and 'h'.

The number 749736 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A157377: a(n) = 531441*n - 313146.

Number of the day: 4548893344

Properties of the number 4548893344:

4548893344 = 2⁵ × 1889 × 75253 is the 4334179637^th composite number and is not squarefree.
4548893344 has 3 distinct prime factors, 24 divisors, 15 antidivisors and 2273212416 totatives.
Reversing the decimal digits of 4548893344 results in a sphenic number.
4548893344 = 1137223337² - 1137223335² = 568611670² - 568611666² = 284305838² - 284305830² = 142152925² - 142152909² = 603913² - 600135² = 304790² - 297234² = 158062² - 142950² = 90365² - 60141² is the difference of 2 nonnegative squares in 8 ways.
4548893344 is the sum of 2 positive triangular numbers.
4548893344 is the difference of 2 positive pentagonal numbers in 2 ways.
4548893344 = 41980² + 52788² = 6412² + 67140² is the sum of 2 positive squares in 2 ways.
4548893344 = 960² + 2812² + 67380² is the sum of 3 positive squares.
4548893344² = 3157013856² + 3275010560² = 1024252544² + 4432080480² = 861003360² + 4466665856² = 2480060544² + 3813362080² is the sum of 2 positive squares in 4 ways.
4548893344² is the sum of 3 positive squares.
4548893344 is a proper divisor of 331⁵⁰¹⁶⁸ - 1.

Number of the day: 58483

Properties of the number 58483:

58483 is a cyclic number.
58483 = 233 × 251 is semiprime and squarefree.
58483 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 58000 totatives.
58483 has a triangular digit sum 28 in base 10.
Reversing the decimal digits of 58483 results in a sphenic number.
58483 = 29242² - 29241² = 242² - 9² is the difference of 2 nonnegative squares in 2 ways.
58483 is the difference of 2 positive pentagonal numbers in 1 way.
58483 = 17² + 87² + 225² is the sum of 3 positive squares.
58483² = 26355² + 52208² is the sum of 2 positive squares in 1 way.
58483² is the sum of 3 positive squares.
58483 is a proper divisor of 503²⁹ - 1.
58483 is an emirpimes in (at least) the following bases: 5, 6, 8, 11, 14, 15, 16, 17, 20, 22, 25, 26, 27, 29, 33, 34, 38, 39, 41, 43, 46, 48, 50, 51, 54, 55, 56, 58, 59, 61, 64, 70, 72, 75, 76, 77, 81, 86, 87, 91, 92, and 99.
58483 is palindromic in (at least) the following bases: 45, 73, and -56.
58483 in base 45 = SdS and consists of only the digits 'S' and 'd'.
58483 in base 55 = JII and consists of only the digits 'I' and 'J'.

The number 58483 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A058518: Number of forests of B-trees of order 3 with n labeled leaves.
A069969: Numbers n such that phi(reverse(n)) = phi(reverse(n-1)) + phi(reverse(n-2)).
A249109: Composite numbers whose sum of aliquot parts divides the sum of the aliquot parts of the numbers less than or equal to n and not relatively prime to n.
A275251: Sequence of pairwise relatively prime numbers of class P_6 (see comment in A275246).

Number of the day: 717853

Properties of the number 717853:

717853 = 23³ × 59 is the 659972^th composite number and is not squarefree.
717853 has 2 distinct prime factors, 8 divisors, 31 antidivisors and 675004 totatives.
717853 has an emirp digit sum 31 in base 10.
Reversing the decimal digits of 717853 results in a semiprime.
717853 = 358927² - 358926² = 15617² - 15594² = 6113² - 6054² = 943² - 414² is the difference of 2 nonnegative squares in 4 ways.
717853 is the difference of 2 positive pentagonal numbers in 4 ways.
717853 = 29² + 36² + 846² is the sum of 3 positive squares.
717853² is the sum of 3 positive squares.
717853 is a proper divisor of 827¹⁰⁵⁸ - 1.
717853 = '71' + '7853' is the concatenation of 2 prime numbers.

The number 717853 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A229146: n^3*(5*n+3)/2.

Number of the day: 971

Properties of the number 971:

971 is a cyclic number.
971 is the 164^th prime.
971 has 5 antidivisors and 970 totatives.
971 has an emirp digit sum 17 in base 10.
Reversing the decimal digits of 971 results in an emirp.
971 = 486² - 485² is the difference of 2 nonnegative squares in 1 way.
971 is the difference of 2 positive pentagonal numbers in 1 way.
971 = 1² + 3² + 31² is the sum of 3 positive squares.
971² is the sum of 3 positive squares.
971 is a proper divisor of 239¹⁰ - 1.
971 is an emirp in (at least) the following bases: 3, 4, 7, 8, 10, 15, 16, 17, 23, 25, 33, 35, 37, 38, 41, 42, 43, 46, 49, 50, 53, 54, 55, 57, 59, 62, 64, 69, 70, 73, 77, 81, 82, 86, 87, 89, 93, 97, 98, and 100.
971 is palindromic in (at least) the following bases: 19, -14, and -97.
971 in base 7 = 2555 and consists of only the digits '2' and '5'.
971 in base 13 = 599 and consists of only the digits '5' and '9'.
971 in base 15 = 44b and consists of only the digits '4' and 'b'.
971 in base 18 = 2hh and consists of only the digits '2' and 'h'.
971 in base 19 = 2d2 and consists of only the digits '2' and 'd'.

The number 971 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000928: Irregular primes: p is regular if and only if the numerators of the Bernoulli numbers B_2, B_4, ..., B_{p-3} (A000367) are not divisible by p.
A001913: Full reptend primes: primes with primitive root 10.
A005846: Primes of the form n^2 + n + 41.
A006567: Emirps (primes whose reversal is a different prime).
A007500: Primes whose reversal in base 10 is also prime (called "palindromic primes" by D. Wells, although that name usually refers to A002385). Also called reversible primes.
A030430: Primes of the form 10*n+1.
A046132: Larger member p+4 of cousin primes (p, p+4).
A061955: Numbers n such that n divides the (left) concatenation of all numbers <= n written in base 2 (most significant digit on right).
A141111: Primes of the form 4*x^2+x*y-4*y^2 (as well as of the form 4*x^2+9*x*y+y^2).
A235266: Primes whose base 2 representation is also the base 3 representation of a prime.

Number of the day: 3505

Properties of the number 3505:

3505 = 5 × 701 is semiprime and squarefree.
3505 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 2800 totatives.
3505 has an emirp digit sum 13 in base 10.
3505 has a Fibonacci digit sum 13 in base 10.
Reversing the decimal digits of 3505 results in an emirpimes.
3505 = 14² + … + 23² is the sum of at least 2 consecutive positive squares in 1 way.
3505 = 1753² - 1752² = 353² - 348² is the difference of 2 nonnegative squares in 2 ways.
3505 is the difference of 2 positive pentagonal numbers in 2 ways.
3505 = 36² + 47² = 16² + 57² is the sum of 2 positive squares in 2 ways.
3505 = 24² + 25² + 48² is the sum of 3 positive squares.
3505² = 2103² + 2804² = 1824² + 2993² = 913² + 3384² = 1300² + 3255² is the sum of 2 positive squares in 4 ways.
3505² is the sum of 3 positive squares.
3505 is a proper divisor of 911⁵ - 1.
3505 is an emirpimes in (at least) the following bases: 4, 7, 10, 12, 13, 15, 16, 17, 18, 23, 26, 27, 29, 31, 37, 38, 39, 42, 45, 50, 51, 57, 61, 62, 65, 66, 68, 69, 71, 73, 74, 75, 79, 84, 87, 88, 89, 91, 92, 93, and 100.
3505 is palindromic in (at least) the following bases: 19, 22, 25, 34, 48, -8, -28, and -73.
3505 in base 8 = 6661 and consists of only the digits '1' and '6'.
3505 in base 19 = 9d9 and consists of only the digits '9' and 'd'.
3505 in base 21 = 7jj and consists of only the digits '7' and 'j'.
3505 in base 22 = 757 and consists of only the digits '5' and '7'.
3505 in base 25 = 5f5 and consists of only the digits '5' and 'f'.
3505 in base 29 = 44p and consists of only the digits '4' and 'p'.
3505 in base 33 = 377 and consists of only the digits '3' and '7'.
3505 in base 34 = 313 and consists of only the digits '1' and '3'.
3505 in base 47 = 1RR and consists of only the digits '1' and 'R'.
3505 in base 48 = 1P1 and consists of only the digits '1' and 'P'.

The number 3505 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006367: Number of binary vectors of length n+1 beginning with 0 and containing just 1 singleton.
A013979: Expansion of 1/(1 - x^2 - x^3 - x^4) = 1/((1 + x)*(1 - x - x^3)).
A026905: Partial sums of the partition numbers A000041.
A072573: Odd interprimes not divisible by 3.
A098237: Composite de Polignac numbers (A006285).
A107458: G.f.: (1-x^2-x^3)/( (1+x)(1-x-x^3) ).
A136392: 6n^2 - 10n + 5.
A182840: Toothpick sequence on hexagonal net.
A205477: L.g.f.: Sum_{n>=1} (x^n/n) * Product_{d|n} (1 + n*x^d/d).
A248112: Number T(n,k) of subsets of {1,...,n} containing n and having at least one set partition into k blocks with equal element sum; triangle T(n,k), n>=1, 1<=k<=floor((n+1)/2), read by rows.

Number of the day: 82545

Properties of the number 82545:

82545 = 3 × 5 × 5503 is a sphenic number and squarefree.
82545 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 44016 totatives.
82545 = 41273² - 41272² = 13759² - 13756² = 8257² - 8252² = 2759² - 2744² is the difference of 2 nonnegative squares in 4 ways.
82545 is the difference of 2 positive pentagonal numbers in 2 ways.
82545 = 17² + 40² + 284² is the sum of 3 positive squares.
82545² = 49527² + 66036² is the sum of 2 positive squares in 1 way.
82545² is the sum of 3 positive squares.
82545 is a proper divisor of 929⁶ - 1.
82545 = '82' + '545' is the concatenation of 2 semiprime numbers.
82545 in base 14 = 22121 and consists of only the digits '1' and '2'.

The number 82545 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A255550: Main diagonal of array A255551.

Number of the day: 45171

Properties of the number 45171:

45171 = 3³ × 7 × 239 is the 40482^th composite number and is not squarefree.
45171 has 3 distinct prime factors, 16 divisors, 23 antidivisors and 25704 totatives.
45171 = 22586² - 22585² = 7530² - 7527² = 3230² - 3223² = 2514² - 2505² = 1086² - 1065² = 850² - 823² = 390² - 327² = 214² - 25² is the difference of 2 nonnegative squares in 8 ways.
45171 is the sum of 2 positive triangular numbers.
45171 is the difference of 2 positive pentagonal numbers in 1 way.
45171 = 11² + 79² + 197² is the sum of 3 positive squares.
45171² is the sum of 3 positive squares.
45171 is a proper divisor of 757¹⁷ - 1.
45171 = '45' + '171' is the concatenation of 2 triangular numbers.
45171 in base 42 = PPL and consists of only the digits 'L' and 'P'.

The number 45171 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A031795: Period of continued fraction for sqrt(n) contains exactly 27 ones.
A050833: Numbers n such that 163*2^n-1 is a prime.
A095053: Number of primes with number of 1-bits equal to one plus number 0-bits (A095073) in range ]2^2n,2^(2n+1)].
A151350: Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 0), (0, 1), (1, -1), (1, 1)}
A188381: Negabinary Keith numbers.
A241639: Number of partitions p of n such that (number of even numbers in p) >= (number of odd numbers in p).

Number of the day: 995361

Johann Bernoulli was born on this day 350 years ago.

Properties of the number 995361:

995361 = 3 × 257 × 1291 is a sphenic number and squarefree.
995361 has 3 distinct prime factors, 8 divisors, 17 antidivisors and 660480 totatives.
995361 has a semiprime digit sum 33 in base 10.
Reversing the decimal digits of 995361 results in a sphenic number.
995361 = 497681² - 497680² = 165895² - 165892² = 2065² - 1808² = 1031² - 260² is the difference of 2 nonnegative squares in 4 ways.
995361 is the sum of 2 positive triangular numbers.
995361 is the difference of 2 positive pentagonal numbers in 2 ways.
995361 = 80² + 169² + 980² is the sum of 3 positive squares.
995361² = 123936² + 987615² is the sum of 2 positive squares in 1 way.
995361² is the sum of 3 positive squares.
995361 is a proper divisor of 1543¹⁵ - 1.
995361 = '995' + '361' is the concatenation of 2 semiprime numbers.

Number of the day: 677201

Niels Henrik Abel was born on this day 215 years ago.

Properties of the number 677201:

677201 is a cyclic number.
677201 = 7 × 89 × 1087 is a sphenic number and squarefree.
677201 has 3 distinct prime factors, 8 divisors, 27 antidivisors and 573408 totatives.
677201 has a prime digit sum 23 in base 10.
677201 = 338601² - 338600² = 48375² - 48368² = 3849² - 3760² = 855² - 232² is the difference of 2 nonnegative squares in 4 ways.
677201 is the difference of 2 positive pentagonal numbers in 4 ways.
677201 = 24² + 65² + 820² is the sum of 3 positive squares.
677201² = 296751² + 608720² is the sum of 2 positive squares in 1 way.
677201² is the sum of 3 positive squares.
677201 is a proper divisor of 257¹³² - 1.
677201 is palindromic in (at least) base -40.

Number of the day: 3119

William Rowan Hamilton was born on this day 212 years ago.

John Venn was born on this day 183 years ago.

Properties of the number 3119:

3119 is a cyclic number.
3119 and 3121 form a twin prime pair.
3119 has 21 antidivisors and 3118 totatives.
3119 has a semiprime digit sum 14 in base 10.
Reversing the decimal digits of 3119 results in a semiprime.
3119 = 1560² - 1559² is the difference of 2 nonnegative squares in 1 way.
3119 is the difference of 2 positive pentagonal numbers in 1 way.
3119 is not the sum of 3 positive squares.
3119² is the sum of 3 positive squares.
3119 is a proper divisor of 2¹⁵⁵⁹ - 1.
3119 = '31' + '19' is the concatenation of 2 prime numbers.
3119 is an emirp in (at least) the following bases: 2, 5, 15, 17, 19, 20, 24, 25, 27, 39, 42, 44, 46, 47, 51, 56, 58, 59, 68, 71, 72, 73, 76, 79, 81, 83, 85, 87, 88, 91, 92, 95, 97, and 100.
3119 is palindromic in (at least) the following bases: -15, and -38.
3119 in base 5 = 44434 and consists of only the digits '3' and '4'.
3119 in base 55 = 11d and consists of only the digits '1' and 'd'.

The number 3119 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001126: Primes with 7 as smallest primitive root.
A001154: Describe the previous term! (method A - initial term is 9).
A024770: Right-truncatable primes: every prefix is prime.
A045709: Primes with first digit 3.
A059452: Safe primes (A005385) which are not Sophie Germain primes.
A060229: Smaller member of a twin prime pair whose mean is a multiple of A002110(3)=30.
A068652: Numbers such that every cyclic permutation is a prime.
A142463: a(n) = 2*n^2 + 2*n - 1.
A164288: Members of A164368 which are not Ramanujan primes.
A215419: Primes that remain prime when a single digit 3 is inserted between any two consecutive digits or as the leading or trailing digit.

Number of the day: 960

Properties of the number 960:

960 = 2⁶ × 3 × 5 is the 797^th composite number and is not squarefree.
960 has 3 distinct prime factors, 28 divisors, 7 antidivisors and 256 totatives.
960 has an emirpimes digit sum 15 in base 10.
960 has a triangular digit sum 15 in base 10.
960 = 6² + … + 14² is the sum of at least 2 consecutive positive squares in 1 way.
960 is the difference of 2 nonnegative squares in 10 ways.
960 is the difference of 2 positive pentagonal numbers in 1 way.
960 is not the sum of 3 positive squares.
960² = 576² + 768² is the sum of 2 positive squares in 1 way.
960² is the sum of 3 positive squares.
960 is a proper divisor of 31² - 1.
960 is palindromic in (at least) the following bases: 31, 39, 47, 59, 63, 79, and 95.
960 in base 4 = 33000 and consists of only the digits '0' and '3'.
960 in base 15 = 440 and consists of only the digits '0' and '4'.

The number 960 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000118: Number of ways of writing n as a sum of 4 squares; also theta series of lattice Z^4.
A002093: Highly abundant numbers: numbers n such that sigma(n) > sigma(m) for all m < n.
A002417: 4-dimensional figurate numbers: a(n) = n*binomial(n+2, 3).
A005179: Smallest number with exactly n divisors.
A005563: a(n) = n*(n+2) (or, (n+1)^2 - 1).
A025487: List giving least integer of each prime signature; also products of primorial numbers A002110.
A029470: Numbers n such that n divides the (right) concatenation of all numbers <= n written in base 25 (most significant digit on left).
A033996: 8 times triangular numbers: a(n) = 4n(n+1).
A051682: 11-gonal (or hendecagonal) numbers: a(n) = n*(9*n-7)/2.
A075928: List of codewords in binary lexicode with Hamming distance 4 written as decimal numbers.

Number of the day: 73457

Properties of the number 73457:

73457 is a cyclic number.
73457 = 17 × 29 × 149 is a sphenic number and squarefree.
73457 has 3 distinct prime factors, 8 divisors, 15 antidivisors and 66304 totatives.
73457 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 73457 results in a prime.
73457 = (48 × 49)/2 + … + (81 × 82)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
73457 = 36729² - 36728² = 2169² - 2152² = 1281² - 1252² = 321² - 172² is the difference of 2 nonnegative squares in 4 ways.
73457 is the difference of 2 positive pentagonal numbers in 4 ways.
73457 = 89² + 256² = 4² + 271² = 184² + 199² = 124² + 241² is the sum of 2 positive squares in 4 ways.
73457 = 14² + 19² + 270² is the sum of 3 positive squares.
73457² = 34568² + 64815² = 10295² + 72732² = 49068² + 54665² = 23095² + 69732² = 2168² + 73425² = 45568² + 57615² = 19668² + 70775² = 5745² + 73232² = 42705² + 59768² = 50660² + 53193² = 29393² + 67320² = 32640² + 65807² = 25143² + 69020² is the sum of 2 positive squares in 13 ways.
73457² is the sum of 3 positive squares.
73457 is a proper divisor of 701²⁸ - 1.
73457 = '7' + '3457' is the concatenation of 2 prime numbers.
73457 = '734' + '57' is the concatenation of 2 semiprime numbers.
73457 is palindromic in (at least) the following bases: 2, and 42.
73457 in base 42 = fQf and consists of only the digits 'Q' and 'f'.
73457 in base 56 = NNf and consists of only the digits 'N' and 'f'.

The number 73457 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A090508: Least number beginning with prime(n) such that every concatenation is a prime.
A253131: Number of length 3+2 0..n arrays with the sum of medians of adjacent triples multiplied by some arrangement of +-1 equal to zero