A364099 - OEIS

A364099

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

1, 3, 4, 5, 6, 7, 8, 11, 10, 11, 12, 13, 14, 20, 16, 17, 18, 19, 20, 27, 22, 23, 24, 25, 29, 34, 28, 29, 30, 31, 32, 41, 34, 35, 36, 44, 38, 48, 40, 41, 42, 43, 44, 55, 46, 47, 56, 49, 50, 62, 52, 57, 54, 55, 56, 69, 58, 68, 60, 61, 62, 76, 64, 65, 66, 67, 68, 92, 80, 71, 72, 73, 74

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..73.

FORMULA

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

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

MATHEMATICA

a[n_] := DivisorSum[5*n - 4, # + 4 &, Mod[#, 5] == 1 &]/5; Array[a, 100] (* Amiram Eldar, Jul 17 2023 *)

PROG

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