Tuesday, January 23, 2018

Number of the day: 66928017519

David Hilbert was born on this day 156 years ago.

Properties of the number 66928017519:

66928017519 = 32 × 11 × 17 × 397 × 100169 is composite and not squarefree.
66928017519 has 5 distinct prime factors, 48 divisors, 55 antidivisors and 38079866880 totatives.
66928017519 is the difference of 2 nonnegative squares in 24 ways.
66928017519 is the difference of 2 positive pentagonal numbers in 7 ways.
66928017519 is not the sum of 3 positive squares.
669280175192 = 314955376562 + 590541331052 = 252680952152 + 619748569442 = 373903195052 + 555096706562 = 302559462812 + 596987206202 = 239688919802 + 624888129692 = 362234327402 + 562780814312 = 81317194202 + 664321809692 = 12704057192 + 669159592202 = 149071446812 + 652467360602 = 384372493562 + 547899387752 = 326108093852 + 584456554442 = 438577093352 + 505555225562 = 68692604312 + 665745656402 is the sum of 2 positive squares in 13 ways.
669280175192 is the sum of 3 positive squares.
66928017519 is a proper divisor of 97179080 - 1.
66928017519 = '6692801' + '7519' is the concatenation of 2 semiprime numbers.

Monday, January 22, 2018

Number of the day: 157757

Properties of the number 157757:

157757 = 193 × 23 is the 143255th composite number and is not squarefree.
157757 has 2 distinct prime factors, 8 divisors, 19 antidivisors and 142956 totatives.
Reversing the decimal digits of 157757 results in a prime.
157757 = 788792 - 788782 = 41612 - 41422 = 34412 - 34182 = 3992 - 382 is the difference of 2 nonnegative squares in 4 ways.
157757 is the difference of 2 positive pentagonal numbers in 3 ways.
157757 = 102 + 292 + 3962 is the sum of 3 positive squares.
1577572 is the sum of 3 positive squares.
157757 is a proper divisor of 115157 - 1.
157757 = '157' + '757' is the concatenation of 2 prime numbers.
157757 = '1577' + '57' is the concatenation of 2 semiprime numbers.

Sunday, January 21, 2018

Number of the day: 7775

Properties of the number 7775:

7775 = 52 × 311 is the 6789th composite number and is not squarefree.
7775 has 2 distinct prime factors, 6 divisors, 11 antidivisors and 6200 totatives.
7775 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 7775 results in a semiprime.
7775 = 65 - 15 is the difference of 2 positive fifth powers in 1 way.
7775 = 38882 - 38872 = 7802 - 7752 = 1682 - 1432 is the difference of 2 nonnegative squares in 3 ways.
7775 is the difference of 2 positive pentagonal numbers in 3 ways.
7775 is not the sum of 3 positive squares.
77752 = 46652 + 62202 = 21772 + 74642 is the sum of 2 positive squares in 2 ways.
77752 is the sum of 3 positive squares.
7775 is a proper divisor of 88110 - 1.
7775 is palindromic in (at least) the following bases: 6, 37, -42, and -58.
7775 in base 6 = 55555 and consists of only the digit '5'.
7775 consists of only the digits '5' and '7'.
7775 in base 36 = 5zz and consists of only the digits '5' and 'z'.
7775 in base 37 = 5P5 and consists of only the digits '5' and 'P'.

The number 7775 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A014946: Numbers n such that n divides 6^n-1.
A024062: a(n) = 6^n-1.
A037205: a(n) = (n+1)^n - 1.
A079907: Numbers n such that 11*12^n -1 is prime.
A104621: Heptanacci-Lucas numbers.
A116632: Positive integers n such that 13^n == 7 (mod n).
A140811: 6n^2 - 1.
A141530: 4*n^3-6*n^2+1
A181288: Numbers of the form i*6^j-1 (i=1..5, j >= 0).
A292737: Numbers in which 7 outnumbers all other digits together.

Saturday, January 20, 2018

Number of the day: 21928

Properties of the number 21928:

21928 = 23 × 2741 is the 19470th composite number and is not squarefree.
21928 has 2 distinct prime factors, 8 divisors, 21 antidivisors and 10960 totatives.
21928 has a semiprime digit sum 22 in base 10.
21928 = 54832 - 54812 = 27432 - 27392 is the difference of 2 nonnegative squares in 2 ways.
21928 is the difference of 2 positive pentagonal numbers in 2 ways.
21928 = 422 + 1422 is the sum of 2 positive squares in 1 way.
21928 = 782 + 882 + 902 is the sum of 3 positive squares.
219282 = 119282 + 184002 is the sum of 2 positive squares in 1 way.
219282 is the sum of 3 positive squares.
21928 is a proper divisor of 44920 - 1.
21928 is palindromic in (at least) the following bases: -35, and -84.
21928 in base 28 = rr4 and consists of only the digits '4' and 'r'.
21928 in base 34 = iww and consists of only the digits 'i' and 'w'.

The number 21928 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002257: Numbers n such that 13*4^n + 1 is prime.
A036063: Increasing gaps among twin primes: size.
A075454: Integer averages of two successive perfect powers (pp(n) + pp(n+1))/2.
A093928: a(n) = sum( A073698(k), k=1...n )^(1/n).
A198016: Number of isomorphism classes of nanocones with 4 pentagons and a nearsymmetric boundary of length n
A233075: Numbers that are midway between the nearest square and the nearest cube.
A235893: T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2X2 subblock
A238869: Number of partitions of n where the difference between consecutive parts is at most 9.
A252201: T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row, column, diagonal and antidiagonal sum not equal to 0 3 5 6 or 7
A261228: a(n) = number of steps to reach 0 when starting from k = (n^3)-1 and repeatedly applying the map that replaces k with k - A055401(k), where A055401(k) = the number of positive cubes needed to sum to k using the greedy algorithm.

Friday, January 19, 2018

Number of the day: 56620484836

Properties of the number 56620484836:

56620484836 = 22 × 5507 × 2570387 is composite and not squarefree.
56620484836 has 3 distinct prime factors, 12 divisors, 23 antidivisors and 28305090632 totatives.
Reversing the decimal digits of 56620484836 results in a sphenic number.
56620484836 = 141551212102 - 141551212082 = 25758942 - 25648802 is the difference of 2 nonnegative squares in 2 ways.
56620484836 is the sum of 2 positive triangular numbers.
56620484836 is the difference of 2 positive pentagonal numbers in 2 ways.
56620484836 = 25342 + 34562 + 2379122 is the sum of 3 positive squares.
566204848362 is the sum of 3 positive squares.
56620484836 is a proper divisor of 64114530334 - 1.

Thursday, January 18, 2018

Number of the day: 103841936

Properties of the number 103841936:

103841936 = 24 × 11 × 167 × 3533 is the 97872092th composite number and is not squarefree.
103841936 has 4 distinct prime factors, 40 divisors, 13 antidivisors and 46904960 totatives.
103841936 has a semiprime digit sum 35 in base 10.
103841936 = 303 + 2943 + 4283 = 653 + 2393 + 4483 is the sum of 3 positive cubes in 2 ways.
103841936 is the difference of 2 nonnegative squares in 12 ways.
103841936 is the difference of 2 positive pentagonal numbers in 4 ways.
103841936 = 3162 + 8242 + 101522 is the sum of 3 positive squares.
1038419362 = 443231362 + 939074402 is the sum of 2 positive squares in 1 way.
1038419362 is the sum of 3 positive squares.
103841936 is a proper divisor of 166917660 - 1.
103841936 = '10384193' + '6' is the concatenation of 2 semiprime numbers.

Wednesday, January 17, 2018

Number of the day: 475395

Properties of the number 475395:

475395 = 3 × 5 × 41 × 773 is the 435744th composite number and is squarefree.
475395 has 4 distinct prime factors, 16 divisors, 21 antidivisors and 247040 totatives.
475395 has a semiprime digit sum 33 in base 10.
Reversing the decimal digits of 475395 results in a sphenic number.
475395 = 2376982 - 2376972 = 792342 - 792312 = 475422 - 475372 = 158542 - 158392 = 58182 - 57772 = 19942 - 18712 = 12622 - 10572 = 6942 - 792 is the difference of 2 nonnegative squares in 8 ways.
475395 is the difference of 2 positive pentagonal numbers in 3 ways.
475395 = 72 + 252 + 6892 is the sum of 3 positive squares.
4753952 = 1947962 + 4336532 = 791012 + 4687682 = 2978912 + 3704882 = 1043552 + 4638002 = 160202 + 4751252 = 2179802 + 4224752 = 3084272 + 3617642 = 2071922 + 4278692 = 2722592 + 3897122 = 2852372 + 3803162 = 1800722 + 4399712 = 2960612 + 3719522 = 1199252 + 4600202 is the sum of 2 positive squares in 13 ways.
4753952 is the sum of 3 positive squares.
475395 is a proper divisor of 12294 - 1.