A189120 Sum of squares of nonprime divisors of n.

1, 1, 1, 17, 1, 37, 1, 81, 82, 101, 1, 197, 1, 197, 226, 337, 1, 442, 1, 517, 442, 485, 1, 837, 626, 677, 811, 997, 1, 1262, 1, 1361, 1090, 1157, 1226, 1898, 1, 1445, 1522, 2181, 1, 2438, 1, 2437, 2332, 2117, 1, 3397, 2402, 3226, 2602, 3397, 1, 4087, 3026, 4197, 3250, 3365

Offset: 1

Author

Jonathan Vos Post, Apr 17 2011

Keywords

• nonn
• easy

Comments

a(p) = 1 for p prime.

Examples

			a(12) = 197 because the divisors of 12 are {1, 2, 3, 4, 6, 12}, the subset of nonprime divisors are {1, 4, 6, 12}, and 1^2 + 4^2 + 6^2 + 12^2 = 197.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A023890 (sum of the nonprime divisors of n).

Cf. A001157, A005063.

Programs

Maple

A189120 := proc(n) local a,d; a := 0 ; for d in numtheory[divisors](n) do if not isprime(d) then a := a+d^2 ; end if; end do: a ; end proc: # R. J. Mathar, Apr 17 2011

Mathematica

Table[Total[Select[Divisors[n], ! PrimeQ[#] &]^2], {n, 50}]

Formula

a(n) = Sum_{k|n, k not prime} k^2.

G.f.: Sum_{k>=1} k^2*x^(k+1)/(1 - x^k) - prime(k)^2*x^(prime(k)+1)/(1 - x^prime(k)). - Ilya Gutkovskiy, Jan 01 2017

a(n) = A001157(n) - A005063(n). - Wesley Ivan Hurt, Sep 04 2022