A363037 - OEIS

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

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OFFSET

1,9

LINKS

Table of n, a(n) for n=1..105.

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).

MATHEMATICA

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

PROG

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