A364032 Expansion of Sum_{k>0} x^(3*k) / (1 + x^(4*k)).

0, 0, 1, 0, 0, 1, -1, 0, 1, 0, 1, 1, 0, -1, 0, 0, 0, 1, 1, 0, 0, 1, -1, 1, 0, 0, 2, -1, 0, 0, -1, 0, 2, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, -1, -1, 1, -1, 0, 2, 0, 0, 2, 0, -1, 2, 0, 1, 0, 0, -1, -1, 0, 0, 2, 1, 0, 0, 0, -1, 1, 0, 0, 1, 1, 0, 0, -1, 0, 2, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 1, 0, -1, 3, 0, 0

Offset: 1

Author

Seiichi Manyama, Jul 01 2023

Keywords

• sign

Crossrefs

Cf. A364033.

Programs

Mathematica

a[n_] := DivisorSum[n, (-1)^((# - 3)/4) &, Mod[#, 4] == 3 &]; Array[a, 100] (* Amiram Eldar, Jul 03 2023 *)

PARI

a(n) = sumdiv(n, d, (d%4==3)*(-1)^((d-3)/4));

Formula

G.f.: Sum_{k>0} (-1)^(k-1) * x^(4*k-1) / (1 - x^(4*k-1)).

a(n) = Sum_{d|n, d==3 (mod 4)} (-1)^((d-3)/4).