## Paul Cohen was born on this day 83 years ago.

### Properties of the number 22750:

22750 = 2 × 5^{3}× 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 = 15

^{2}+ 86

^{2}+ 123

^{2}is the sum of 3 positive squares.

22750

^{2}= 8750

^{2}+ 21000

^{2}= 5600

^{2}+ 22050

^{2}= 11550

^{2}+ 19600

^{2}= 14280

^{2}+ 17710

^{2}= 2520

^{2}+ 22610

^{2}= 798

^{2}+ 22736

^{2}= 15582

^{2}+ 16576

^{2}= 13650

^{2}+ 18200

^{2}= 6370

^{2}+ 21840

^{2}= 8008

^{2}+ 21294

^{2}is the sum of 2 positive squares in 10 ways.

22750

^{2}is the sum of 3 positive squares.

22750 is a divisor of 307

^{4}- 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).

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