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

1,4

Comments

a(p) = 1 for p prime.

Links

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

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

Example

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.

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}]

Crossrefs

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

Cf. A001157, A005063.

Sequence in context: A124517 A241121 A040305 * A102292 A264439 A279363

Adjacent sequences: A189117 A189118 A189119 * A189121 A189122 A189123

Keyword

nonn,easy

Author

Jonathan Vos Post, Apr 17 2011

Status

approved