A363970 Expansion of Sum_{k>0} k^2 * x^(3*k-2) / (1 - x^(3*k-2)).

1, 1, 1, 5, 1, 1, 10, 5, 1, 17, 1, 5, 26, 10, 1, 41, 1, 1, 50, 21, 10, 65, 1, 5, 82, 26, 1, 114, 1, 17, 122, 41, 1, 145, 10, 5, 170, 50, 26, 217, 1, 10, 226, 69, 1, 257, 1, 41, 299, 98, 1, 354, 1, 1, 362, 114, 50, 401, 1, 21, 442, 122, 10, 525, 26, 65, 530, 149, 1, 602, 1, 5, 626, 170

Offset

1,4

Links

Table of n, a(n) for n=1..74.

Formula

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

Mathematica

a[n_] := DivisorSum[n, ((#+2)/3)^2 &, Mod[#, 3] == 1 &]; Array[a, 100] (* Amiram Eldar, Jun 30 2023 *)

Prog

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

Crossrefs

Cf. A001817, A363901.

Cf. A103637, A363975.

Sequence in context: A279003 A210651 A255831 * A356113 A188461 A188474

Adjacent sequences: A363967 A363968 A363969 * A363971 A363972 A363973

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 30 2023

Status

approved