A364033 Expansion of Sum_{k>0} k * x^(3*k) / (1 + x^(4*k)).

0, 0, 1, 0, 0, 2, -1, 0, 3, 0, 1, 4, 0, -2, 4, 0, 0, 6, 1, 0, 4, 2, -1, 8, 0, 0, 10, -4, 0, 8, -1, 0, 14, 0, -4, 12, 0, 2, 12, 0, 0, 8, 1, 4, 12, -2, -1, 16, -7, 0, 18, 0, 0, 20, 4, -8, 22, 0, 1, 16, 0, -2, 11, 0, 0, 28, 1, 0, 20, -8, -1, 24, 0, 0, 21, 4, -4, 24, -1, 0, 30, 0, 1, 16, 0, 2, 28, 8, 0, 24, -12

Offset: 1

Author

Seiichi Manyama, Jul 01 2023

Keywords

• sign

Crossrefs

Cf. A364032.

Programs

Mathematica

a[n_] := DivisorSum[n, (-1)^((#-3)/4) * (n/#) &, Mod[#, 4] == 3 &]; Array[a, 100] (* Amiram Eldar, Jul 02 2023 *)

PARI

a(n) = sumdiv(n, d, (d%4==3)*(-1)^((d-3)/4)*n/d);

Formula

G.f.: Sum_{k>0} (-1)^(k-1) * x^(4*k-1) / (1 - x^(4*k-1))^2.

a(n) = Sum_{d|n, d==3 (mod 4)} (-1)^((d-3)/4) * (n/d).