A363926 Expansion of Sum_{k>0} x^(2*k) / (1 - x^(5*k))^2.

0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 4, 0, 3, 0, 1, 4, 1, 0, 1, 2, 6, 0, 4, 0, 1, 6, 3, 0, 1, 0, 8, 0, 5, 2, 4, 8, 1, 0, 1, 0, 12, 0, 6, 0, 1, 10, 4, 2, 1, 4, 12, 0, 7, 0, 3, 12, 1, 0, 4, 0, 14, 2, 8, 0, 6, 14, 5, 0, 3, 0, 19, 0, 9, 0, 1, 18, 1, 0, 1, 6, 18, 0, 15, 4, 1, 18, 6, 0, 1, 2, 20, 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, A363928, A363929.

Cf. A001877, A284280.

Programs

Mathematica

a[n_] := DivisorSum[n, # + 3 &, Mod[#, 5] == 2 &] / 5; Array[a, 100] (* Amiram Eldar, Jun 28 2023 *)

PARI

a(n) = sumdiv(n, d, (d%5==2)*(d+3))/5;

Formula

a(n) = (1/5) * Sum_{d|n, d==2 mod 5} (d+3) = (3 * A001877(n) + A284280(n))/5.

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