A363629 Expansion of Sum_{k>0} (1/(1+x^k)^2 - 1).

-2, 1, -6, 6, -8, 4, -10, 15, -16, 6, -14, 22, -16, 8, -28, 32, -20, 13, -22, 32, -36, 12, -26, 56, -34, 14, -44, 42, -32, 24, -34, 65, -52, 18, -52, 68, -40, 20, -60, 82, -44, 32, -46, 62, -84, 24, -50, 122, -60, 31, -76, 72, -56, 40, -76, 108, -84, 30, -62, 124, -64, 32, -110, 130, -88, 48, -70, 92

Offset: 1

Author

Seiichi Manyama, Jun 12 2023

Keywords

• sign
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A363630, A363631.

Cf. A002129, A048272, A325940.

Programs

Mathematica

a[n_] := DivisorSum[n, (-1)^#*(# + 1) &]; Array[a, 100] (* Amiram Eldar, Jul 18 2023 *)

PARI

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

Formula

G.f.: Sum_{k>0} (k+1) * (-x)^k/(1 - x^k).

a(n) = Sum_{d|n} (-1)^d * (d+1) = -(A002129(n) + A048272(n)).