A363901 Expansion of Sum_{k>0} x^k / (1 - x^(3*k))^2.

1, 1, 1, 3, 1, 1, 4, 3, 1, 5, 1, 3, 6, 4, 1, 9, 1, 1, 8, 7, 4, 9, 1, 3, 10, 6, 1, 16, 1, 5, 12, 9, 1, 13, 4, 3, 14, 8, 6, 21, 1, 4, 16, 11, 1, 17, 1, 9, 21, 14, 1, 26, 1, 1, 20, 16, 8, 21, 1, 7, 22, 12, 4, 31, 6, 9, 24, 15, 1, 32, 1, 3, 26, 14, 10, 36, 4, 6, 28, 27, 1, 29, 1, 16, 30, 16, 1, 41, 1

Offset: 1

Author

Seiichi Manyama, Jun 27 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A001817, A078181.

Cf. A113415, A363903.

Programs

Mathematica

a[n_] := DivisorSum[n, # + 2 &, Mod[#, 3] == 1 &]/3; Array[a, 100] (* Amiram Eldar, Jun 27 2023 *)

PARI

a(n) = sumdiv(n, d, (d%3==1)*(d+2))/3;

Formula

a(n) = (1/3) * Sum_{d|n, d==1 mod 3} (d+2) = (2 * A001817(n) + A078181(n))/3.

G.f.: Sum_{k>0} k * x^(3*k-2) / (1 - x^(3*k-2)).