A364046 Expansion of Sum_{k>0} x^(4*k) / (1 + x^(5*k)).

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

Offset: 1

Author

Seiichi Manyama, Jul 03 2023

Keywords

• sign

Crossrefs

Cf. A364043, A364044, A364045.

Cf. A001899, A364022.

Programs

Mathematica

a[n_] := DivisorSum[n, (-1)^# &, Mod[#, 5] == 4 &]; Array[a, 100] (* Amiram Eldar, Jul 03 2023 *)

PARI

a(n) = sumdiv(n, d, (d%5==4)*(-1)^d);

Formula

G.f.: Sum_{k>0} (-1)^(k-1) * x^(5*k-1) / (1 - x^(5*k-1)).

a(n) = Sum_{d|n, d==4 (mod 5)} (-1)^d.