A363929 Expansion of Sum_{k>0} x^(4*k) / (1 - x^(5*k))^2.

0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1, 0, 3, 0, 1, 0, 2, 4, 1, 0, 0, 0, 6, 0, 0, 2, 4, 6, 0, 0, 1, 0, 7, 0, 3, 0, 4, 8, 1, 0, 3, 0, 10, 2, 0, 0, 6, 10, 0, 0, 1, 0, 13, 0, 4, 4, 6, 12, 1, 0, 0, 2, 14, 0, 0, 0, 8, 14, 3, 0, 8, 0, 15, 0, 5, 0, 8, 16, 1, 2, 0, 0, 21, 0, 0, 6, 10, 18, 2, 0, 1, 0, 19, 4, 6, 0, 13, 22, 1, 0, 7, 0, 22, 0, 0, 0, 14, 22, 0, 0

Offset: 1

Author

Seiichi Manyama, Jun 28 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A363925, A363926, A363928.

Cf. A001899, A284103.

Programs

Mathematica

a[n_] := DivisorSum[n, # + 1 &, Mod[#, 5] == 4 &] / 5; Array[a, 100] (* Amiram Eldar, Jun 28 2023 *)

PARI

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

Formula

a(n) = (1/5) * Sum_{d|n, d==4 mod 5} (d+1) = (A001899(n) + A284103(n))/5.

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