Sunday, October 1, 2017

Number of the day: 23782

Properties of the number 23782:

23782 = 2 × 11 × 23 × 47 is the 21136th 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.

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