A364098 Expansion of Sum_{k>0} k * x^(2*k-1) / (1 - x^(5*k-4)).

1, 1, 3, 1, 4, 1, 5, 1, 8, 1, 7, 1, 8, 1, 11, 4, 10, 1, 11, 1, 14, 1, 17, 1, 14, 1, 20, 1, 16, 6, 17, 1, 20, 1, 19, 1, 26, 4, 27, 1, 22, 1, 23, 8, 26, 1, 25, 1, 29, 1, 42, 1, 28, 1, 33, 1, 32, 10, 31, 4, 32, 1, 41, 1, 44, 1, 35, 1, 38, 1, 44, 17, 38, 1, 48, 1, 40, 1, 53, 1, 44, 4, 43, 1, 44, 14, 59, 1

Offset

1,3

Links

Table of n, a(n) for n=1..88.

Formula

a(n) = (1/5) * Sum_{d | 5*n-3, d==1 (mod 5)} (d+4).

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

Mathematica

a[n_] := DivisorSum[5*n - 3, # + 4 &, Mod[#, 5] == 1 &]/5; Array[a, 100] (* Amiram Eldar, Jul 12 2023 *)

Prog

(PARI) a(n) = sumdiv(5*n-3, d, (d%5==1)*(d+4))/5;

Crossrefs

Cf. A359237, A364094.

Sequence in context: A349042 A302792 A179820 * A363521 A166050 A259655

Adjacent sequences: A364095 A364096 A364097 * A364099 A364100 A364101

Keyword

nonn

Author

Seiichi Manyama, Jul 04 2023

Status

approved