Number of the day: 128751

Karl Weierstrass was born on this day 202 years ago.

Properties of the number 128751:

128751 = 3 × 7 × 6131 is a sphenic number and squarefree.
128751 has 3 distinct prime factors, 8 divisors, 7 antidivisors and 73560 totatives.
Reversing the decimal digits of 128751 results in a sphenic number.
128751 = 64376² - 64375² = 21460² - 21457² = 9200² - 9193² = 3076² - 3055² is the difference of 2 nonnegative squares in 4 ways.
128751 is the sum of 2 positive triangular numbers.
128751 is the difference of 2 positive pentagonal numbers in 2 ways.
128751 is not the sum of 3 positive squares.
128751² is the sum of 3 positive squares.
128751 is a proper divisor of 659¹⁰ - 1.
128751 is palindromic in (at least) the following bases: 68, and 83.
128751 in base 50 = 11P1 and consists of only the digits '1' and 'P'.

Number of the day: 96134

Properties of the number 96134:

96134 = 2 × 71 × 677 is a sphenic number and squarefree.
96134 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 47320 totatives.
96134 has a prime digit sum 23 in base 10.
96134 is the difference of 2 positive pentagonal numbers in 1 way.
96134 = 13² + 22² + 309² is the sum of 3 positive squares.
96134² = 7384² + 95850² is the sum of 2 positive squares in 1 way.
96134² is the sum of 3 positive squares.
96134 is a proper divisor of 1039⁹¹ - 1.
96134 = '9' + '6134' is the concatenation of 2 semiprime numbers.
96134 is palindromic in (at least) base 58.
96134 in base 3 = 11212212112 and consists of only the digits '1' and '2'.
96134 in base 26 = 5c5c and consists of only the digits '5' and 'c'.
96134 in base 58 = SXS and consists of only the digits 'S' and 'X'.

The number 96134 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A020992: a(n) = a(n-1) + a(n-2) + a(n-3).
A145916: Even composites in A145832 with at least three distinct prime factors.
A193912: Partial sums of A193911.

Number of the day: 1634

Properties of the number 1634:

1634 = 2 × 19 × 43 is a sphenic number and squarefree.
1634 has 3 distinct prime factors, 8 divisors, 15 antidivisors and 756 totatives.
1634 has a semiprime digit sum 14 in base 10.
1634 has an oblong digit product 72 in base 10.
1634 is the difference of 2 positive pentagonal pyramidal numbers in 1 way.
1634 = 7² + 8² + 39² is the sum of 3 positive squares.
1634² is the sum of 3 positive squares.
1634 is a proper divisor of 1291² - 1.
1634 is palindromic in (at least) the following bases: 13, 24, 42, 85, -32, -34, and -71.
1634 in base 13 = 989 and consists of only the digits '8' and '9'.
1634 in base 16 = 662 and consists of only the digits '2' and '6'.
1634 in base 24 = 2k2 and consists of only the digits '2' and 'k'.
1634 in base 28 = 22a and consists of only the digits '2' and 'a'.

The number 1634 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002961: Numbers n such that n and n+1 have same sum of divisors.
A003321: Smallest n-th order perfect digital invariant or PDI: smallest number > 1 equal to sum of n-th powers of its digits, or 0 if no such number.
A005188: Armstrong (or Plus Perfect, or narcissistic) numbers: n-digit numbers equal to sum of n-th powers of their digits (a finite sequence, the last term being 115132219018763992565095597973971522401).
A014576: Smallest n-digit narcissistic (or Armstrong) number: smallest n-digit number equal to sum of n-th powers of its digits (or 0 if no such number exists).
A022267: a(n) = n*(9*n + 1)/2.
A023052: Powerful numbers (3): numbers n that are the sum of some fixed power of their digits.
A028557: n(n+5).
A056109: Fifth spoke of a hexagonal spiral.
A252648: Irregular table of perfect digital invariants for n > 1, i.e., numbers equal to the sum of n-th powers of their digits, read by rows.
A268261: T(n,k)=Number of length-(n+1) 0..k arrays with new repeated values introduced in sequential order starting with zero.

Number of the day: 323866

Properties of the number 323866:

323866 = 2 × 83 × 1951 is a sphenic number and squarefree.
323866 has 3 distinct prime factors, 8 divisors, 13 antidivisors and 159900 totatives.
323866 has a triangular digit sum 28 in base 10.
Reversing the decimal digits of 323866 results in a semiprime.
323866 = 3³ + 54³ + 55³ is the sum of 3 positive cubes in 1 way.
323866 is the sum of 2 positive triangular numbers.
323866 is the difference of 2 positive pentagonal numbers in 2 ways.
323866 = 21² + 44² + 567² is the sum of 3 positive squares.
323866² is the sum of 3 positive squares.
323866 is a proper divisor of 499³⁹ - 1.
323866 = '323' + '866' is the concatenation of 2 semiprime numbers.
323866 is palindromic in (at least) the following bases: 82, 94, and -84.

The number 323866 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A114146: Number of threshold functions on n X n grid.

Number of the day: 16769

Properties of the number 16769:

16769 is a cyclic number.
16769 = 41 × 409 is semiprime and squarefree.
16769 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 16320 totatives.
16769 has a prime digit sum 29 in base 10.
Reversing the decimal digits of 16769 results in a sphenic number.
16769 = 8385² - 8384² = 225² - 184² is the difference of 2 nonnegative squares in 2 ways.
16769 is the sum of 2 positive triangular numbers.
16769 is the difference of 2 positive pentagonal numbers in 2 ways.
16769 = 88² + 95² = 65² + 112² is the sum of 2 positive squares in 2 ways.
16769 = 8² + 57² + 116² is the sum of 3 positive squares.
16769² = 8319² + 14560² = 3681² + 16360² = 1281² + 16720² = 4920² + 16031² is the sum of 2 positive squares in 4 ways.
16769² is the sum of 3 positive squares.
16769 is a proper divisor of 1637⁸ - 1.
16769 is an emirpimes in (at least) the following bases: 4, 5, 6, 9, 19, 22, 24, 28, 35, 41, 43, 49, 51, 53, 56, 57, 59, 65, 67, 68, 69, 73, 80, 82, 83, 85, 87, 89, 90, 91, 93, and 100.
16769 is palindromic in (at least) the following bases: 38, 81, -26, and -83.
16769 in base 30 = iit and consists of only the digits 'i' and 't'.
16769 in base 38 = BNB and consists of only the digits 'B' and 'N'.

The number 16769 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A003372: Numbers that are the sum of 5 positive 7th powers.
A010013: a(0) = 1, a(n) = 23*n^2 + 2 for n>0.
A024946: s(n+3)/2, where s is A024945.
A041115: Denominators of continued fraction convergents to sqrt(66).
A041495: Denominators of continued fraction convergents to sqrt(264).
A042139: Denominators of continued fraction convergents to sqrt(594).
A239358: Number of nX5 0..2 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 3
A255967: Odd numbers n that are neither of the form p + 2^k nor of the form p - 2^k with 2^k < n, and p prime.

Number of the day: 5462

Shiing-Shen Chern was born on this day 106 years ago.

Properties of the number 5462:

5462 = 2 × 2731 is semiprime and squarefree.
5462 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 2730 totatives.
5462 has an emirp digit sum 17 in base 10.
5462 has an oblong digit product 240 in base 10.
5462 = 14² + 15² + 71² is the sum of 3 positive squares.
5462² is the sum of 3 positive squares.
5462 is a proper divisor of 683¹³ - 1.
5462 is an emirpimes in (at least) the following bases: 4, 7, 8, 14, 16, 18, 20, 22, 37, 38, 40, 45, 46, 68, 70, 78, 81, 82, 85, 89, 93, 94, 97, and 98.
5462 is palindromic in (at least) the following bases: 52, -4, -23, -27, -31, -60, -65, and -70.
5462 in base 4 = 1111112 and consists of only the digits '1' and '2'.
5462 in base 20 = dd2 and consists of only the digits '2' and 'd'.
5462 in base 22 = b66 and consists of only the digits '6' and 'b'.
5462 in base 26 = 822 and consists of only the digits '2' and '8'.
5462 in base 30 = 622 and consists of only the digits '2' and '6'.
5462 in base 51 = 255 and consists of only the digits '2' and '5'.
5462 in base 52 = 212 and consists of only the digits '1' and '2'.

The number 5462 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005578: a(2*n) = 2*a(2*n-1), a(2*n+1) = 2*a(2*n)-1.
A024494: C(n,1) + C(n,4) + ... + C(n,3[n/3]+1).
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,...
A047849: a(n) = (4^n + 2)/3.
A056105: First spoke of a hexagonal spiral.
A078008: Expansion of (1-x)/(1 - x - 2*x^2).
A131708: A024494 prefixed by a 0.
A151575: G.f.: (1+x)/(1+x-2*x^2).
A231263: T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order
A238555: Number T(n,k) of equivalence classes of ways of placing k 2 X 2 tiles in an n X 7 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=2, 0<=k<=3*floor(n/2), read by rows.

Number of the day: 8951

Évariste Galois was born on this day 206 years ago.

Properties of the number 8951:

8951 is a cyclic number.
8951 is the 1113^th prime.
8951 has 19 antidivisors and 8950 totatives.
8951 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 8951 results in a sphenic number.
8951 = 4476² - 4475² is the difference of 2 nonnegative squares in 1 way.
8951 is the difference of 2 positive pentagonal numbers in 1 way.
8951 is not the sum of 3 positive squares.
8951² is the sum of 3 positive squares.
8951 is a proper divisor of 3²⁵ - 1.
8951 is an emirp in (at least) the following bases: 2, 3, 5, 9, 11, 12, 18, 20, 21, 25, 31, 34, 39, 41, 52, 59, 68, 70, 74, 75, 76, 80, 81, 82, 89, 92, 93, 94, 95, 97, and 100.
8951 is palindromic in (at least) the following bases: 33, 42, 57, and -22.
8951 in base 28 = bbj and consists of only the digits 'b' and 'j'.
8951 in base 31 = 99n and consists of only the digits '9' and 'n'.
8951 in base 32 = 8nn and consists of only the digits '8' and 'n'.
8951 in base 33 = 878 and consists of only the digits '7' and '8'.
8951 in base 41 = 5DD and consists of only the digits '5' and 'D'.
8951 in base 42 = 535 and consists of only the digits '3' and '5'.
8951 in base 54 = 33f and consists of only the digits '3' and 'f'.
8951 in base 56 = 2ll and consists of only the digits '2' and 'l'.
8951 in base 57 = 2h2 and consists of only the digits '2' and 'h'.

The number 8951 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A052283: Triangle read by rows giving numbers of directed graphs by numbers of nodes and arcs.
A060528: A list of equal temperaments (equal divisions of the octave) whose nearest scale steps are closer and closer approximations to the ratios of two tones of musical harmony: the perfect 4th, 4/3 and its complement the perfect 5th, 3/2.
A129733: List of primitive prime divisors of the numbers (3^n-1)/2 (A003462) in their order of occurrence.
A142027: Primes congruent to 23 mod 31.
A165459: Primes p such that the sum of the digits of p^2 is 16.
A189560: Least odd number k such that x' = k has n solutions, where x' is the arithmetic derivative (A003415) of x.
A196202: a(n) = 2^(prime(n)-1) mod prime(n)^2.
A237811: Primes p such that 2*p+1 and 2*p+9 are also prime.
A246342: a(0) = 12, after which, if a(n-1) = product_{k >= 1} (p_k)^(c_k), then a(n) = (1/2) * (1 + product_{k >= 1} (p_{k+1})^(c_k)), where p_k indicates the k-th prime, A000040(k).
A265786: Numerators of upper primes-only best approximates (POBAs) to sqrt(5); see Comments.

Number of the day: 268

Properties of the number 268:

268 = 2² × 67 is the 211^th composite number and is not squarefree.
268 has 2 distinct prime factors, 6 divisors, 5 antidivisors and 132 totatives.
Reversing the decimal digits of 268 results in a semiprime.
268 = 68² - 66² is the difference of 2 nonnegative squares in 1 way.
268 is the sum of 2 positive triangular numbers.
268 is the difference of 2 positive pentagonal numbers in 1 way.
268 = 6² + 6² + 14² is the sum of 3 positive squares.
268² is the sum of 3 positive squares.
268 is a proper divisor of 401² - 1.
268 is palindromic in (at least) the following bases: 8, 66, -14, and -89.
268 in base 8 = 414 and consists of only the digits '1' and '4'.
268 in base 11 = 224 and consists of only the digits '2' and '4'.

The number 268 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001043: Numbers that are the sum of 2 successive primes.
A002371: Period of decimal expansion of 1/(n-th prime) (0 by convention for the primes 2 and 5).
A002822: Numbers n such that 6n-1, 6n+1 are twin primes.
A005114: Untouchable numbers, also called nonaliquot numbers: impossible values for sum of aliquot parts of n (A001065).
A006093: a(n) = prime(n) - 1.
A014263: Numbers that contain even digits only.
A016957: a(n) = 6*n + 4.
A017113: a(n) = 8*n+4.
A054753: Numbers which are the product of a prime and the square of a different prime (p^2 * q).
A246392: Numbers n such that Phi(10, n) is prime, where Phi is the cyclotomic polynomial.

Number of the day: 10232017

Happy Mole Day!

Properties of the number 10232017:

10232017 is a cyclic number.
10232017 = 37 × 131 × 2111 is a sphenic number and squarefree.
10232017 has 3 distinct prime factors, 8 divisors, 23 antidivisors and 9874800 totatives.
Reversing the decimal digits of 10232017 results in a sphenic number.
10232017 = 5116009² - 5116008² = 138289² - 138252² = 39119² - 38988² = 3479² - 1368² is the difference of 2 nonnegative squares in 4 ways.
10232017 is the difference of 2 positive pentagonal numbers in 3 ways.
10232017 = 18² + 67² + 3198² is the sum of 3 positive squares.
10232017² = 3318492² + 9678935² is the sum of 2 positive squares in 1 way.
10232017² is the sum of 3 positive squares.
10232017 is a proper divisor of 787⁶³³ - 1.
10232017 = '10' + '232017' is the concatenation of 2 semiprime numbers.

Number of the day: 99598

Properties of the number 99598:

99598 = 2 × 19 × 2621 is a sphenic number and squarefree.
99598 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 47160 totatives.
Reversing the decimal digits of 99598 results in a prime.
99598 is the sum of 2 positive triangular numbers.
99598 is the difference of 2 positive pentagonal numbers in 4 ways.
99598 = 7² + 18² + 315² is the sum of 3 positive squares.
99598² = 41800² + 90402² is the sum of 2 positive squares in 1 way.
99598² is the sum of 3 positive squares.
99598 is a proper divisor of 761¹⁰ - 1.
99598 = '9' + '9598' is the concatenation of 2 semiprime numbers.
99598 is palindromic in (at least) base -62.
99598 in base 61 = Qkk and consists of only the digits 'Q' and 'k'.

The number 99598 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A137741: Number of different strings of length n+4 obtained from "123...n" by iteratively duplicating any substring.

Number of the day: 249411

Martin Gardner was born on this day 103 years ago.

Properties of the number 249411:

249411 = 3 × 83137 is semiprime and squarefree.
249411 has 2 distinct prime factors, 4 divisors, 7 antidivisors and 166272 totatives.
249411 has a semiprime digit sum 21 in base 10.
249411 has a Fibonacci digit sum 21 in base 10.
249411 has a triangular digit sum 21 in base 10.
Reversing the decimal digits of 249411 results in a sphenic number.
249411 = 124706² - 124705² = 41570² - 41567² is the difference of 2 nonnegative squares in 2 ways.
249411 is the sum of 2 positive triangular numbers.
249411 is the difference of 2 positive pentagonal numbers in 1 way.
249411 = 1² + 49² + 497² is the sum of 3 positive squares.
249411² = 30525² + 247536² is the sum of 2 positive squares in 1 way.
249411² is the sum of 3 positive squares.
249411 is a proper divisor of 1669⁴³³ - 1.
249411 = '2' + '49411' is the concatenation of 2 prime numbers.
249411 = '249' + '411' is the concatenation of 2 semiprime numbers.
249411 is an emirpimes in (at least) the following bases: 2, 3, 15, 20, 21, 23, 27, 28, 33, 37, 39, 40, 42, 48, 51, 59, 63, 65, 67, 74, 75, 81, 84, and 87.
249411 is palindromic in (at least) base -94.

Number of the day: 38795

Properties of the number 38795:

38795 is a cyclic number.
38795 = 5 × 7759 is semiprime and squarefree.
38795 has 2 distinct prime factors, 4 divisors, 13 antidivisors and 31032 totatives.
Reversing the decimal digits of 38795 results in an emirpimes.
38795 = 19398² - 19397² = 3882² - 3877² is the difference of 2 nonnegative squares in 2 ways.
38795 is the difference of 2 positive pentagonal numbers in 2 ways.
38795 = 5² + 39² + 193² is the sum of 3 positive squares.
38795² = 23277² + 31036² is the sum of 2 positive squares in 1 way.
38795² is the sum of 3 positive squares.
38795 is a proper divisor of 1759⁶ - 1.
38795 is an emirpimes in (at least) the following bases: 7, 10, 13, 17, 19, 23, 30, 32, 33, 34, 37, 43, 47, 49, 51, 53, 61, 64, 65, 74, 90, and 97.
38795 is palindromic in (at least) the following bases: 9, 79, and -90.

The number 38795 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A264454: Number of permutations of [n] with exactly five (possibly overlapping) occurrences of the generalized pattern 12-3.
A283886: Relative of Hofstadter Q-sequence: a(n) = max(0, n+19395) for n <= 0; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 0.
A291688: Number of permutations p of [2n] such that 0p has a nonincreasing jump sequence beginning with n.
A292172: Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with six.
A292173: Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with seven.

Number of the day: 586159

Properties of the number 586159:

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

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

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

Number of the day: 94234

Properties of the number 94234:

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

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

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

Number of the day: 467661421

Properties of the number 467661421:

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

Number of the day: 6715453888

Properties of the number 6715453888:

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

Number of the day: 3265527765

Properties of the number 3265527765:

3265527765 = 3 × 5 × 217701851 is a sphenic number and squarefree.
3265527765 has 3 distinct prime factors, 8 divisors, 59 antidivisors and 1741614800 totatives.
3265527765 = 1632763883² - 1632763882² = 544254629² - 544254626² = 326552779² - 326552774² = 108850933² - 108850918² is the difference of 2 nonnegative squares in 4 ways.
3265527765 is the sum of 2 positive triangular numbers.
3265527765 is the difference of 2 positive pentagonal numbers in 2 ways.
3265527765 = 305² + 476² + 57142² is the sum of 3 positive squares.
3265527765² = 1959316659² + 2612422212² is the sum of 2 positive squares in 1 way.
3265527765² is the sum of 3 positive squares.
3265527765 is a proper divisor of 1321^4354037 - 1.

Number of the day: 874427

Properties of the number 874427:

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

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

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

Number of the day: 2108

Properties of the number 2108:

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

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

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

Number of the day: 144655464

Properties of the number 144655464:

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

Number of the day: 9711868390

Properties of the number 9711868390:

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

Number of the day: 9216

Properties of the number 9216:

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

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

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

Number of the day: 9188

Properties of the number 9188:

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

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

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

Number of the day: 198445

Richard Dedekind was born on this day 186 years ago.

Properties of the number 198445:

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

Number of the day: 709383

Properties of the number 709383:

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

Number of the day: 3094

Properties of the number 3094:

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

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

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

Number of the day: 83409

Properties of the number 83409:

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

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

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

Number of the day: 78968

Properties of the number 78968:

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

Number of the day: 23782

Properties of the number 23782:

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

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

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