A363928 Expansion of Sum_{k>0} x^(3*k) / (1 - x^(5*k))^2.

0, 0, 1, 0, 0, 1, 0, 2, 1, 0, 0, 1, 3, 0, 1, 2, 0, 5, 0, 0, 1, 0, 5, 3, 0, 3, 1, 6, 0, 1, 0, 2, 8, 0, 0, 5, 0, 8, 4, 2, 0, 1, 9, 0, 1, 5, 0, 13, 0, 0, 1, 3, 11, 5, 0, 8, 1, 12, 0, 1, 0, 0, 14, 2, 3, 8, 0, 14, 6, 0, 0, 7, 15, 0, 1, 8, 0, 20, 0, 2, 1, 0, 17, 7, 0, 9, 1, 20, 0, 5, 3, 5, 20, 0, 0, 13, 0, 20, 8, 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, A363929.

Cf. A001878, A284281.

Programs

Mathematica

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

PARI

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

Formula

a(n) = (1/5) * Sum_{d|n, d==3 mod 5} (d+2) = (2 * A001878(n) + A284281(n))/5.

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