A364022 Expansion of Sum_{k>0} k * x^(4*k) / (1 + x^(5*k)).

0, 0, 0, 1, 0, 0, 0, 2, -1, 0, 0, 3, 0, 1, 0, 4, 0, -2, -1, 5, 0, 0, 0, 7, 0, 0, -3, 9, -1, 0, 0, 8, 0, 1, 0, 5, 0, -2, -1, 10, 0, 3, 0, 12, -5, 0, 0, 14, -1, 0, 0, 13, 0, -5, 0, 18, -3, -2, -1, 15, 0, 0, -7, 17, 0, 0, 0, 19, -1, 5, 0, 13, 0, 1, 0, 15, 0, -2, -1, 20, -9, 0, 0, 28, 0, 0, -3, 24, -1, -10, 0

Offset: 1

Author

Seiichi Manyama, Jul 01 2023

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A364019, A364020, A364021.

Cf. A363900.

Programs

Mathematica

a[n_] := DivisorSum[n, (-1)^(n/#) * # &, Mod[n/#, 5] == 4 &]; Array[a, 100] (* Amiram Eldar, Jul 03 2023 *)

PARI

a(n) = sumdiv(n, d, (n/d%5==4)*(-1)^(n/d)*d);

Formula

G.f.: Sum_{k>0} (-1)^(k-1) * x^(5*k-1) / (1 - x^(5*k-1))^2.

a(n) = Sum_{d|n, n/d==4 (mod 5)} (-1)^(n/d) * d.