A364097 Expansion of Sum_{k>0} k * x^(3*k-2) / (1 - x^(5*k-4)).

1, 1, 1, 3, 1, 1, 4, 1, 1, 7, 1, 1, 6, 1, 1, 9, 1, 4, 8, 1, 1, 11, 1, 1, 10, 5, 1, 13, 4, 1, 12, 1, 1, 20, 1, 1, 14, 1, 1, 20, 1, 11, 16, 1, 1, 19, 1, 1, 18, 8, 4, 21, 1, 1, 25, 1, 1, 35, 1, 1, 22, 4, 1, 25, 1, 10, 24, 7, 1, 27, 1, 1, 29, 15, 1, 34, 1, 1, 28, 1, 8, 42, 1, 4, 30, 1, 1, 33, 1, 17, 32, 1, 1

Offset

1,4

Links

Table of n, a(n) for n=1..93.

Formula

a(n) = (1/5) * Sum_{d | 5*n-2, d==1 (mod 5)} (d+4).

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

Mathematica

a[n_] := DivisorSum[5*n - 2, # + 4 &, Mod[#, 5] == 1 &]/5; Array[a, 100] (* Amiram Eldar, Jul 12 2023 *)

Prog

(PARI) a(n) = sumdiv(5*n-2, d, (d%5==1)*(d+4))/5;

Crossrefs

Cf. A359236, A364093.

Sequence in context: A111956 A024564 A084795 * A030184 A284373 A104610

Adjacent sequences: A364094 A364095 A364096 * A364098 A364099 A364100

Keyword

nonn

Author

Seiichi Manyama, Jul 04 2023

Status

approved