A364104 - OEIS

A364104

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

1, 2, 3, 4, 6, 6, 7, 8, 10, 10, 13, 12, 14, 14, 15, 16, 21, 18, 19, 22, 22, 22, 27, 24, 26, 26, 27, 28, 37, 30, 34, 32, 34, 34, 41, 36, 38, 40, 39, 40, 49, 46, 43, 44, 49, 46, 57, 48, 50, 50, 51, 52, 68, 54, 55, 58, 58, 58, 72, 60, 66, 62, 63, 70, 79, 66, 67, 68, 70, 70, 83, 72, 77, 76, 82, 76, 96

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OFFSET

1,2

LINKS

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

FORMULA

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

G.f.: Sum_{k>0} x^(4*k-3) / (1 - x^(5*k-4))^2.

MATHEMATICA

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

PROG

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