A239668 Sum of the composite divisors of n^2.

0, 4, 9, 28, 25, 85, 49, 124, 117, 209, 121, 397, 169, 389, 394, 508, 289, 841, 361, 953, 730, 917, 529, 1645, 775, 1265, 1089, 1757, 841, 2810, 961, 2044, 1714, 2129, 1754, 3745, 1369, 2645, 2362, 3929, 1681, 5174, 1849, 4109, 3742, 3845, 2209, 6637, 2793, 5459, 3970

Offset: 1

Author

Janet Lee, Mar 23 2014

Keywords

• nonn

Examples

			For n=2, the sum of the composite factors of n^2 is equal to 4.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A000720, A023891.

Programs

Maple

A008472 := n -> add(d, d = select(isprime, numtheory[divisors](n))):
f:=n->numtheory[sigma](n^2)-A008472(n)-1; [seq(f(n),n=1..100)]; # N. J. A. Sloane, Mar 31 2014

Mathematica

a[n_] := DivisorSum[n^2, If[# == 1 || PrimeQ[#], 0, #]& ]; Array[a, 60] (* Jean-François Alcover, Dec 18 2015 *)
Table[Total[Select[Divisors[n^2],CompositeQ]],{n,60}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 06 2017 *)

PARI

a(n) = sumdiv(n^2, d, d*(!isprime(d) && (d != 1))); \\ Michel Marcus, Mar 31 2014

Formula

a(n) = sigma(n^2) - sopf(n^2) - 1.

a(n) = A000203(n^2) - A008472(n^2) - 1. - Wesley Ivan Hurt, Mar 30 2014

a(n) = A023891(n^2). - Michel Marcus, Mar 31 2014

a(n) = n^2 if n is prime. - Zak Seidov, Mar 31 2014

Extensions

Formula corrected by Wesley Ivan Hurt, Mar 30 2014

More terms from N. J. A. Sloane, Mar 31 2014