A364043 Expansion of Sum_{k>0} x^k / (1 + x^(5*k)).

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

Offset: 1

Author

Seiichi Manyama, Jul 03 2023

Keywords

• sign

Crossrefs

Cf. A364044, A364045, A364046.

Cf. A002654, A363037, A364011, A364047.

Cf. A001876, A364019.

Programs

Mathematica

a[n_] := -DivisorSum[n, (-1)^# &, Mod[#, 5] == 1 &]; Array[a, 100] (* Amiram Eldar, Jul 05 2023 *)

PARI

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

Formula

G.f.: Sum_{k>0} (-1)^(k-1) * x^(5*k-4) / (1 - x^(5*k-4)).

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