Number of the day: 22750

Paul Cohen was born on this day 83 years ago.

Properties of the number 22750:

22750 = 2 × 5³ × 7 × 13 is the 20207^th composite number and is not squarefree.
22750 has 4 distinct prime factors, 32 divisors, 23 antidivisors and 7200 totatives.
22750 is the sum of 2 positive triangular numbers.
22750 is the difference of 2 positive pentagonal numbers in 9 ways.
22750 = 15² + 86² + 123² is the sum of 3 positive squares.
22750² = 8750² + 21000² = 5600² + 22050² = 11550² + 19600² = 14280² + 17710² = 2520² + 22610² = 798² + 22736² = 15582² + 16576² = 13650² + 18200² = 6370² + 21840² = 8008² + 21294² is the sum of 2 positive squares in 10 ways.
22750² is the sum of 3 positive squares.
22750 is a divisor of 307⁴ - 1.
22750 is palindromic in (at least) the following bases: 57, 94, and -57.
22750 in base 18 = 3g3g and consists of only the digits '3' and 'g'.
22750 in base 56 = 7EE and consists of only the digits '7' and 'E'.
22750 in base 57 = 707 and consists of only the digits '0' and '7'.
22750 in base 61 = 66w and consists of only the digits '6' and 'w'.

The number 22750 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A032387: Numbers n such that 75*2^n+1 is prime.
A052963: a(0)=1, a(1)=2, a(2)=5, a(n) = 3*a(n+2) - a(n+3).
A079816: Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=1, r=5, I={1}.
A095661: Fifth column (m=4) of (1,3)-Pascal triangle A095660.
A135036: Sums of the products of n consecutive pairs of numbers.
A167566: The third left hand column of triangle A167565.
A190048: Expansion of (8+6*x)/(1-x)^5
A213496: Number of (w,x,y) with all terms in {0,...,n} and x != max(|w-x|,|x-y|)
A274453: Products of distinct numbers in A052963.
A283237: a(n) = sigma_2(3*n).