A363155 Expansion of Sum_{k>0} k * x^(3*k-1) / (1 - x^(5*k-2)).

0, 1, 0, 0, 3, 0, 0, 4, 0, 0, 5, 0, 2, 6, 0, 0, 7, 0, 0, 8, 5, 0, 9, 0, 0, 10, 0, 0, 17, 0, 0, 12, 0, 3, 13, 0, 7, 14, 0, 0, 15, 0, 0, 16, 8, 0, 24, 0, 0, 18, 0, 0, 28, 0, 0, 20, 0, 0, 21, 8, 10, 22, 0, 0, 27, 0, 0, 24, 11, 0, 25, 0, 9, 26, 0, 0, 39, 0, 0, 28, 0, 0, 38, 0, 13, 40, 0, 0, 31, 0, 0

Offset: 1

Author

Seiichi Manyama, Jul 06 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A359288, A363033.

Cf. A363028, A364096, A364104.

Programs

Mathematica

a[n_] := DivisorSum[5*n - 1, # + 2 &, Mod[#, 5] == 3 &]/5; Array[a, 100] (* Amiram Eldar, Jul 06 2023 *)

PARI

a(n) = sumdiv(5*n-1, d, (d%5==3)*(d+2))/5;

Formula

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

G.f.: Sum_{k>0} x^(3*k-1) / (1 - x^(5*k-2))^2.