A362683 Expansion of Sum_{k>0} (1/(1 - k*x^k)^2 - 1).

2, 7, 10, 25, 16, 78, 22, 153, 136, 298, 34, 1254, 40, 1214, 2004, 3825, 52, 11385, 58, 20894, 18932, 25006, 70, 150002, 18826, 115274, 199828, 389510, 88, 1334624, 94, 1725281, 2131188, 2360266, 725948, 14878299, 112, 10486958, 22329428, 37317986, 124, 120957336, 130

Offset: 1

Author

Seiichi Manyama, Jun 13 2023

Keywords

• nonn

Crossrefs

Cf. A338662, A363639, A363640.

Cf. A007503, A055225, A359103, A363646.

Programs

Mathematica

a[n_] := DivisorSum[n, (n/#)^# * (# + 1) &]; Array[a, 50] (* Amiram Eldar, Jul 17 2023 *)

PARI

a(n) = sumdiv(n, d, (n/d)^d*(d+1));

Formula

a(n) = Sum_{d|n} (n/d)^d * (d+1) = A055225(n) + A359103(n).

If p is prime, a(p) = 1 + 3*p.