A363156 Expansion of Sum_{k>0} k * x^k / (1 - x^(5*k-2)).

1, 2, 3, 5, 5, 6, 8, 8, 9, 13, 11, 12, 14, 14, 15, 20, 17, 20, 20, 20, 21, 27, 23, 24, 26, 28, 27, 34, 32, 30, 32, 32, 33, 43, 35, 36, 38, 38, 39, 52, 41, 47, 44, 44, 45, 55, 47, 48, 50, 52, 56, 62, 53, 54, 59, 56, 57, 75, 59, 60, 62, 68, 63, 76, 65, 68, 68, 71, 69, 83, 71, 72, 81, 81, 75, 94, 77, 78, 80

Offset

1,2

Links

Table of n, a(n) for n=1..79.

Formula

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A359236, A363034.

Sequence in context: A346616 A333645 A066113 * A214881 A364085 A163831

Adjacent sequences: A363153 A363154 A363155 * A363157 A363158 A363159

Keyword

nonn

Author

Seiichi Manyama, Jul 06 2023

Status

approved