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A189120 Sum of squares of nonprime divisors of n. 2
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 (list; graph; refs; listen; history; text; internal format)
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 and 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

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).

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

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Last modified June 17 06:06 EDT 2019. Contains 324183 sequences. (Running on oeis4.)