Number of the day: 27610

John Forbes Nash, Jr. was born on this day 90 years ago.

Properties of the number 27610:

27610 = 2 × 5 × 11 × 251 is the 24597^th composite number and is squarefree.
27610 has 4 distinct prime factors, 16 divisors, 13 antidivisors and 10000 totatives.
27610 = 45² + … + 55² is the sum of at least 2 consecutive positive squares in 1 way.
27610 is the sum of 2 positive triangular numbers.
27610 is the difference of 2 positive pentagonal numbers in 3 ways.
27610 = 40² + 51² + 153² is the sum of 3 positive squares.
27610² = 16566² + 22088² is the sum of 2 positive squares in 1 way.
27610² is the sum of 3 positive squares.
27610 is a proper divisor of 149¹⁰ - 1.
27610 = '276' + '10' is the concatenation of 2 triangular numbers.
27610 is palindromic in (at least) the following bases: 32, 67, -41, -42, and -86.
27610 in base 32 = quq and consists of only the digits 'q' and 'u'.
27610 in base 40 = HAA and consists of only the digits 'A' and 'H'.
27610 in base 41 = GHH and consists of only the digits 'G' and 'H'.
27610 in base 52 = AAo and consists of only the digits 'A' and 'o'.

The number 27610 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A182724: Sum of all parts of all partitions of n minus the number of partitions of n.
A207255: Number of 4Xn 0..1 arrays avoiding 0 0 1 and 1 0 1 horizontally and 0 1 0 and 1 0 1 vertically
A242691: Number of partitions of n with difference -1 between the number of odd parts and the number of even parts, both counted without multiplicity.
A248114: Number of subsets of {1,...,n} containing n and having at least one set partition into 5 blocks with equal element sum.