A364020 Expansion of Sum_{k>0} k * x^(2*k) / (1 + x^(5*k)).

0, 1, 0, 2, 0, 3, -1, 4, 0, 5, 0, 7, 0, 5, 0, 8, -1, 9, 0, 10, -3, 12, 0, 14, 0, 13, -1, 10, 0, 15, 0, 17, 0, 15, -5, 21, -1, 19, 0, 20, 0, 16, 0, 24, 0, 23, -1, 28, -7, 25, -3, 27, 0, 25, 0, 20, -1, 29, 0, 35, 0, 32, -9, 34, 0, 36, -1, 30, 0, 25, 0, 43, 0, 35, 0, 38, -12, 39, 0, 40, -3, 42, 0, 39, -5, 43, -1

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, A364021, A364022.

Cf. A363898.

Programs

Mathematica

a[n_] := DivisorSum[n, (-1)^(n/#) * # &, Mod[n/#, 5] == 2 &]; Array[a, 100] (* Amiram Eldar, Jul 03 2023 *)

PARI

a(n) = sumdiv(n, d, (n/d%5==2)*(-1)^(n/d)*d);

Formula

G.f.: Sum_{k>0} (-1)^(k-1) * x^(5*k-3) / (1 - x^(5*k-3))^2.

a(n) = Sum_{d|n, n/d==2 (mod 5)} (-1)^(n/d) * d.