A364082 Expansion of Sum_{k>0} k * x^(3*k-2) / (1 - x^(4*k-3)).

1, 1, 1, 3, 1, 1, 4, 1, 3, 5, 1, 1, 6, 3, 1, 10, 1, 1, 10, 1, 1, 9, 5, 3, 13, 1, 1, 11, 3, 6, 12, 1, 1, 18, 1, 5, 20, 1, 3, 15, 1, 1, 19, 10, 1, 17, 6, 1, 24, 1, 9, 22, 1, 3, 20, 1, 1, 36, 3, 1, 25, 5, 1, 30, 11, 1, 24, 1, 10, 28, 1, 12, 26, 3, 5, 27, 1, 1, 51, 9, 6, 29, 1, 3, 30, 14, 1, 38, 3, 1, 41, 1, 15, 42, 1, 1

Offset: 1

Author

Seiichi Manyama, Jul 04 2023

Keywords

• nonn

Crossrefs

Cf. A078703.

Programs

Mathematica

a[n_] := DivisorSum[4*n - 1, # + 3 &, Mod[#, 4] == 1 &]/4; Array[a, 100] (* Amiram Eldar, Jul 05 2023 *)

PARI

a(n) = sumdiv(4*n-1, d, (d%4==1)*(d+3))/4;

Formula

a(n) = (1/4) * Sum_{d | 4*n-1, d==1 (mod 4)} (d+3).

G.f.: Sum_{k>0} x^k / (1 - x^(4*k-1))^2.