A363925 Expansion of Sum_{k>0} x^k / (1 - x^(5*k))^2.

1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 4, 3, 1, 1, 1, 5, 1, 3, 1, 1, 6, 4, 1, 3, 1, 7, 1, 1, 1, 3, 8, 5, 4, 1, 1, 11, 1, 1, 1, 1, 10, 8, 1, 4, 1, 11, 1, 7, 1, 1, 12, 7, 1, 3, 4, 13, 1, 1, 1, 3, 14, 8, 6, 5, 1, 20, 1, 1, 1, 1, 16, 11, 1, 1, 1, 17, 4, 9, 1, 5, 18, 10, 1, 8, 1, 19, 1, 4, 1, 3, 20, 11

Offset: 1

Author

Seiichi Manyama, Jun 28 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A363926, A363928, A363929.

Cf. A001876, A284097.

Cf. A363901, A363903.

Programs

Mathematica

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

PARI

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

Formula

a(n) = (1/5) * Sum_{d|n, d==1 mod 5} (d+4) = (4 * A001876(n) + A284097(n))/5.

G.f.: Sum_{k>0} k * x^(5*k-4) / (1 - x^(5*k-4)).