A363649 Expansion of Sum_{k>0} x^(2*k)/(1 - (k*x)^k)^2.

0, 1, 2, 4, 4, 14, 6, 56, 62, 266, 10, 3991, 12, 6158, 84996, 225296, 16, 2881607, 18, 96995583, 87740548, 2621462, 22, 30762215703, 122070312524, 50331674, 84457666628, 8631957089039, 28, 885639790229244, 30, 2814753793638432, 76826598191124

Offset

1,3

Links

Table of n, a(n) for n=1..33.

Formula

a(n) = Sum_{d|n} (n/d)^(n-2*n/d) * (d-1).

If p is prime, a(p) = p - 1.

Mathematica

a[n_] := DivisorSum[n, (n/#)^(n-2*n/#) * (#-1) &]; Array[a, 33] (* Amiram Eldar, Jul 18 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, (n/d)^(n-2*n/d)*(d-1));

Crossrefs

Cf. A359112, A363646.

Cf. A363641.

Sequence in context: A154987 A089419 A341235 * A263023 A193848 A371254

Adjacent sequences: A363646 A363647 A363648 * A363650 A363651 A363652

Keyword

nonn

Author

Seiichi Manyama, Jun 13 2023

Status

approved