A363030 Expansion of Sum_{k>0} k * x^k / (1 - x^(5*k-3)).

1, 2, 4, 4, 6, 6, 8, 8, 12, 10, 12, 12, 14, 14, 19, 18, 18, 18, 20, 20, 26, 22, 26, 24, 26, 26, 36, 28, 30, 32, 32, 32, 40, 34, 36, 36, 40, 42, 50, 40, 42, 42, 44, 46, 54, 46, 48, 48, 55, 50, 66, 52, 54, 54, 60, 56, 68, 60, 60, 66, 62, 62, 78, 64, 68, 66, 68, 68, 82, 70, 84, 78, 74, 74, 92, 76, 78

Offset

1,2

Links

Table of n, a(n) for n=1..77.

Formula

a(n) = (1/5) * Sum_{d | 5*n-3, d==2 (mod 5)} (d+3).

G.f.: Sum_{k>0} x^(2*k-1) / (1 - x^(5*k-4))^2.

Mathematica

a[n_] := DivisorSum[5*n - 3, # + 3 &, Mod[#, 5] == 2 &]/5; Array[a, 100] (* Amiram Eldar, Jul 06 2023 *)

Prog

(PARI) a(n) = sumdiv(5*n-3, d, (d%5==2)*(d+3))/5;

Crossrefs

Cf. A359237, A363026.

Sequence in context: A210466 A085914 A211390 * A014684 A113638 A187323

Adjacent sequences: A363027 A363028 A363029 * A363031 A363032 A363033

Keyword

nonn

Author

Seiichi Manyama, Jul 06 2023

Status

approved