A363037 Expansion of Sum_{k>0} x^k / (1 + x^(4*k)).

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

Offset: 1

Author

Seiichi Manyama, Jul 01 2023

Keywords

• nonn

Crossrefs

Cf. A002654, A364011.

Cf. A364031, A364032.

Programs

Mathematica

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

PARI

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

Formula

G.f.: Sum_{k>0} (-1)^(k-1) * x^(4*k-3) / (1 - x^(4*k-3)).

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