Monday, December 5, 2016

Number of the day: 50521760

Properties of the number 50521760:

50521760 = 25 × 5 × 19 × 16619 is the 47491233th composite number and is not squarefree.
50521760 has 4 distinct prime factors, 48 divisors, 15 antidivisors and 19143936 totatives.
50521760 has an emirpimes digit sum 26 in base 10.
50521760 is the difference of 2 nonnegative squares in 16 ways.
50521760 is the difference of 2 positive pentagonal numbers in 3 ways.
50521760 = 1002 + 4642 + 70922 is the sum of 3 positive squares.
505217602 = 303130562 + 404174082 is the sum of 2 positive squares in 1 way.
505217602 is the sum of 3 positive squares.
50521760 is a divisor of 5694748 - 1.

Sunday, December 4, 2016

Number of the day: 9824198521655

Properties of the number 9824198521655:

9824198521655 = 5 × 7 × 239 × 1174440947 is composite and squarefree.
9824198521655 has 4 distinct prime factors, 16 divisors, 19 antidivisors and 6708406683552 totatives.
9824198521655 has a semiprime digit sum 65 in base 10.
9824198521655 = 49120992608282 - 49120992608272 = 9824198521682 - 9824198521632 = 7017284658362 - 7017284658292 = 1403456931842 - 1403456931492 = 205527166922 - 205527164532 = 41105439122 - 41105427172 = 29361032042 - 29361015312 = 5872246562 - 5872162912 is the difference of 2 nonnegative squares in 8 ways.
9824198521655 is the difference of 2 positive pentagonal numbers in 8 ways.
9824198521655 is not the sum of 3 positive squares.
98241985216552 = 58945191129932 + 78593588173242 is the sum of 2 positive squares in 1 way.
98241985216552 is the sum of 3 positive squares.
9824198521655 is a divisor of 1657803979708 - 1.
9824198521655 = '982' + '4198521655' is the concatenation of 2 emirpimes.
9824198521655 = '98241985' + '21655' is the concatenation of 2 sphenic numbers.

Saturday, December 3, 2016

Number of the day: 88566360628

Properties of the number 88566360628:

88566360628 = 22 × 22141590157 is composite and not squarefree.
88566360628 has 2 distinct prime factors, 6 divisors, 69 antidivisors and 44283180312 totatives.
88566360628 has an emirpimes digit sum 58 in base 10.
88566360628 = 221415901582 - 221415901562 is the difference of 2 nonnegative squares in 1 way.
88566360628 is the sum of 2 positive triangular numbers.
88566360628 is the difference of 2 positive pentagonal numbers in 1 way.
88566360628 = 2022682 + 2182982 is the sum of 2 positive squares in 1 way.
88566360628 = 16742 + 34762 + 2975762 is the sum of 3 positive squares.
885663606282 = 67416729802 + 883093997282 is the sum of 2 positive squares in 1 way.
885663606282 is the sum of 3 positive squares.
88566360628 is a divisor of 10516631204 - 1.

Friday, December 2, 2016

Number of the day: 2621

Properties of the number 2621:

2621 is the 381th prime.
2621 has 7 antidivisors and 2620 totatives.
2621 has a prime digit sum 11 in base 10.
Reversing the decimal digits of 2621 results in a semiprime.
2621 = 13112 - 13102 is the difference of 2 nonnegative squares in 1 way.
2621 is the sum of 2 positive triangular numbers.
2621 is the difference of 2 positive pentagonal numbers in 1 way.
2621 = 112 + 502 is the sum of 2 positive squares in 1 way.
2621 = 112 + 142 + 482 is the sum of 3 positive squares.
26212 = 11002 + 23792 is the sum of 2 positive squares in 1 way.
26212 is the sum of 3 positive squares.
2621 is a divisor of 76110 - 1.
2621 = '26' + '21' is the concatenation of 2 semiprime numbers.
2621 is an emirp in (at least) the following bases: 3, 5, 7, 11, 12, 13, 19, 21, 25, 26, 29, 31, 37, 41, 42, 43, 45, 47, 51, 53, 55, 58, 60, 69, 70, 71, 81, 84, 88, 90, 93, 94, 95, and 99.
2621 is palindromic in (at least) the following bases: 15, -10, -24, and -34.
2621 in base 15 = b9b and consists of only the digits '9' and 'b'.
2621 in base 25 = 44l and consists of only the digits '4' and 'l'.
2621 in base 29 = 33b and consists of only the digits '3' and 'b'.

The number 2621 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A007641: Primes of form 2n^2+29.
A096700: Balanced primes of order eight.
A099970: Write 1/e as a binary fraction; read this from left to right and whenever a 1 appears, note the integer formed by reading leftwards from that 1. Then divide these numbers by 2.
A107132: Primes of the form 2x^2+13y^2.
A117876: Primes p=prime(k) of level (1,2), i.e. such that A118534(k) = prime(k-2).
A124575: Triangle read by rows: row n is the first row of the matrix M[n]^(n-1), where M[n] is the n X n tridiagonal matrix with main diagonal (2,4,4,...) and super- and subdiagonals (1,1,1,...).
A141881: Primes congruent to 1 mod 20.
A164288: Members of A164368 which are not Ramanujan primes.
A164294: Primes prime(k) such that all integers in [(prime(k-1)+1)/2,(prime(k)-1)/2] are composite, excluding those primes in A080359.
A261718: Number A(n,k) of partitions 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.

Thursday, December 1, 2016

Number of the day: 882600

Nikolai Lobachevsky was born on this day 224 years ago.

Properties of the number 882600:

882600 = 23 × 3 × 52 × 1471 is the 812582th composite number and is not squarefree.
882600 has 4 distinct prime factors, 48 divisors, 15 antidivisors and 235200 totatives.
882600 is the difference of 2 nonnegative squares in 12 ways.
882600 is the sum of 2 positive triangular numbers.
882600 is the difference of 2 positive pentagonal numbers in 2 ways.
882600 = 802 + 2022 + 9142 is the sum of 3 positive squares.
8826002 = 5295602 + 7060802 = 2471282 + 8472962 is the sum of 2 positive squares in 2 ways.
8826002 is the sum of 3 positive squares.
882600 is a divisor of 2516 - 1.
882600 is palindromic in (at least) the following bases: 74, and -97.

Wednesday, November 30, 2016

Number of the day: 696557958264193

Properties of the number 696557958264193:

696557958264193 = 67 × 159857 × 65035547 is a sphenic number and squarefree.
696557958264193 has 3 distinct prime factors, 8 divisors, 73 antidivisors and 686157267930816 totatives.
696557958264193 has an emirpimes digit sum 85 in base 10.
696557958264193 = 3482789791320972 - 3482789791320962 = 51981937184232 - 51981937183562 = 21787707532 - 21786108962 = 378729832 - 271625642 is the difference of 2 nonnegative squares in 4 ways.
696557958264193 is the sum of 2 positive triangular numbers.
696557958264193 is the difference of 2 positive pentagonal numbers in 4 ways.
696557958264193 = 702 + 344432 + 263923622 is the sum of 3 positive squares.
6965579582641932 = 4266094503453452 + 5506336042208322 is the sum of 2 positive squares in 1 way.
6965579582641932 is the sum of 3 positive squares.
696557958264193 is a divisor of 1847160767869712 - 1.
696557958264193 = '69' + '6557958264193' is the concatenation of 2 semiprime numbers.

Tuesday, November 29, 2016

Number of the day: 96075

Properties of the number 96075:

96075 = 32 × 52 × 7 × 61 is the 86816th composite number and is not squarefree.
96075 has 4 distinct prime factors, 36 divisors, 41 antidivisors and 43200 totatives.
96075 is the difference of 2 nonnegative squares in 18 ways.
96075 is the sum of 2 positive triangular numbers.
96075 is the difference of 2 positive pentagonal numbers in 4 ways.
96075 = 52 + 1012 + 2932 is the sum of 3 positive squares.
960752 = 428402 + 859952 = 173252 + 945002 = 430922 + 858692 = 652052 + 705602 = 98282 + 955712 = 576452 + 768602 = 269012 + 922322 is the sum of 2 positive squares in 7 ways.
960752 is the sum of 3 positive squares.
96075 is a divisor of 10516 - 1.
96075 is palindromic in (at least) the following bases: -57, and -86.
96075 in base 7 = 550050 and consists of only the digits '0' and '5'.
96075 in base 56 = UZZ and consists of only the digits 'U' and 'Z'.