A364096 Expansion of Sum_{k>0} k * x^(4*k-3) / (1 - x^(5*k-4)).

1, 1, 1, 1, 3, 1, 1, 1, 4, 1, 3, 1, 5, 1, 1, 1, 8, 1, 1, 4, 7, 1, 3, 1, 8, 1, 1, 1, 15, 1, 4, 1, 10, 1, 3, 1, 11, 6, 1, 1, 14, 4, 1, 1, 17, 1, 9, 1, 14, 1, 1, 1, 20, 1, 1, 8, 16, 1, 8, 1, 21, 1, 1, 4, 28, 1, 1, 1, 19, 1, 3, 1, 26, 10, 4, 1, 27, 1, 1, 6, 22, 1, 13, 1, 23, 4, 8, 1, 26, 1, 1, 12, 29, 1, 3, 1

Offset: 1

Author

Seiichi Manyama, Jul 04 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A359233, A364092.

Cf. A363028, A363155, A364104.

Programs

Mathematica

a[n_] := DivisorSum[5*n - 1, # + 4 &, Mod[#, 5] == 1 &]/5; Array[a, 100] (* Amiram Eldar, Jul 12 2023 *)

PARI

a(n) = sumdiv(5*n-1, d, (d%5==1)*(d+4))/5;

Formula

a(n) = (1/5) * Sum_{d | 5*n-1, d==1 (mod 5)} (d+4).

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