A363028 Expansion of Sum_{k>0} k * x^(2*k-1) / (1 - x^(5*k-3)).

1, 0, 3, 0, 4, 0, 5, 0, 6, 2, 7, 0, 8, 0, 9, 0, 15, 0, 11, 0, 12, 0, 13, 6, 14, 0, 15, 0, 19, 0, 24, 0, 18, 0, 19, 0, 20, 8, 21, 0, 29, 0, 23, 0, 33, 0, 25, 0, 26, 0, 27, 10, 36, 0, 29, 0, 30, 4, 42, 0, 32, 0, 33, 0, 43, 12, 35, 0, 36, 0, 37, 0, 51, 0, 48, 0, 50, 0, 41, 14, 42, 0, 43, 0, 44, 0, 60, 0

Offset

1,3

Links

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

Formula

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

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

Mathematica

a[n_] := DivisorSum[5*n - 1, # + 3 &, Mod[#, 5] == 2 &]/5; Array[a, 100] (* Amiram Eldar, Jul 06 2023 *)

Prog

(PARI) a(n) = sumdiv(5*n-1, d, (d%5==2)*(d+3))/5;

Crossrefs

Cf. A359287, A362952.

Cf. A363155, A364096, A364104.

Sequence in context: A359866 A297217 A218859 * A364067 A246691 A066705

Adjacent sequences: A363025 A363026 A363027 * A363029 A363030 A363031

Keyword

nonn

Author

Seiichi Manyama, Jul 06 2023

Status

approved