A363157 Expansion of Sum_{k>0} k * x^(4*k-1) / (1 - x^(5*k-2)).

0, 0, 1, 0, 0, 1, 2, 0, 1, 0, 3, 1, 0, 0, 7, 0, 0, 1, 5, 0, 1, 0, 8, 4, 0, 0, 8, 0, 0, 1, 10, 0, 5, 0, 9, 1, 3, 0, 13, 0, 0, 6, 11, 0, 1, 0, 14, 1, 0, 3, 24, 0, 0, 1, 16, 0, 1, 0, 15, 8, 0, 0, 22, 0, 5, 1, 17, 0, 13, 0, 20, 1, 0, 0, 20, 3, 0, 10, 28, 0, 1, 0, 21, 1, 0, 0, 39, 5, 3, 1, 23, 0, 8, 0, 26, 12, 0, 0, 26

Offset: 1

Author

Seiichi Manyama, Jul 06 2023

Keywords

• nonn

Crossrefs

Cf. A359270, A363035.

Programs

Mathematica

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

PARI

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

Formula

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

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