A364083 Expansion of Sum_{k>0} k * x^k / (1 - x^(4*k-3)).

1, 3, 4, 5, 6, 7, 10, 9, 10, 11, 12, 18, 14, 15, 16, 17, 24, 19, 20, 21, 25, 30, 24, 25, 26, 27, 36, 29, 30, 38, 32, 42, 34, 35, 36, 37, 48, 39, 48, 41, 42, 54, 48, 45, 46, 47, 60, 58, 50, 51, 52, 66, 54, 55, 56, 66, 82, 59, 60, 61, 62, 78, 64, 65, 66, 78, 84, 69, 80, 71, 72, 90, 79, 75, 88, 77, 96

Offset: 1

Author

Seiichi Manyama, Jul 04 2023

Keywords

• nonn

Crossrefs

Cf. A359227.

Programs

Mathematica

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

PARI

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

Formula

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

G.f.: Sum_{k>0} x^k / (1 - x^(4*k-3))^2.