A363900 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, 13, 0, 2, 1, 10, 0, 3, 0, 12, 5, 0, 0, 14, 1, 0, 0, 13, 0, 7, 0, 18, 3, 2, 1, 15, 0, 0, 7, 17, 0, 0, 0, 19, 1, 5, 0, 29, 0, 1, 0, 23, 0, 2, 1, 20, 9, 0, 0, 28, 0, 0, 3, 24, 1, 10, 0, 23, 0, 1, 5, 28, 0

Offset: 1

Author

Seiichi Manyama, Jun 27 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A363897, A363898, A363899.

Cf. A001899, A284103.

Programs

Mathematica

a[n_] := DivisorSum[n, # &, Mod[n/#, 5] == 4 &]; Array[a, 100] (* Amiram Eldar, Jun 27 2023 *)

PARI

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

Formula

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

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