A364048 Expansion of Sum_{k>0} x^(5*k) / (1 + x^(6*k)).

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

Offset: 1

Author

Seiichi Manyama, Jul 03 2023

Keywords

• sign

Crossrefs

Cf. A319995.

Programs

Mathematica

a[n_] := DivisorSum[n, (-1)^((#-5)/6) &, Mod[#, 6] == 5 &]; Array[a, 100] (* Amiram Eldar, Jul 03 2023 *)

PARI

a(n) = sumdiv(n, d, (d%6==5)*(-1)^((d-5)/6));

Formula

G.f.: Sum_{k>0} (-1)^(k-1) * x^(6*k-1) / (1 - x^(6*k-1)).

a(n) = Sum_{d|n, d==5 (mod 6)} (-1)^((d-5)/6).