A363902 Expansion of Sum_{k>0} x^(2*k) / (1 - x^(3*k))^2.

0, 1, 0, 1, 2, 1, 0, 4, 0, 3, 4, 1, 0, 6, 2, 4, 6, 1, 0, 10, 0, 5, 8, 4, 2, 10, 0, 6, 10, 3, 0, 15, 4, 7, 14, 1, 0, 14, 0, 13, 14, 6, 0, 20, 2, 9, 16, 4, 0, 20, 6, 10, 18, 1, 6, 28, 0, 11, 20, 10, 0, 22, 0, 15, 24, 5, 0, 30, 8, 20, 24, 4, 0, 26, 2, 14, 30, 10, 0, 40, 0, 15, 28, 6, 8

Offset: 1

Author

Seiichi Manyama, Jun 27 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A001822, A078182, A363901.

Cf. A113415, A363904.

Programs

Mathematica

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

PARI

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

Formula

a(n) = (1/3) * Sum_{d|n, d==2 mod 3} (d+1) = (A001822(n) + A078182(n))/3.

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