A363971 Expansion of Sum_{k>0} k^2 * x^(3*k-1) / (1 - x^(3*k-1)).

0, 1, 0, 1, 4, 1, 0, 10, 0, 5, 16, 1, 0, 26, 4, 10, 36, 1, 0, 54, 0, 17, 64, 10, 4, 82, 0, 26, 100, 5, 0, 131, 16, 37, 148, 1, 0, 170, 0, 63, 196, 26, 0, 242, 4, 65, 256, 10, 0, 294, 36, 82, 324, 1, 20, 396, 0, 101, 400, 54, 0, 442, 0, 131, 488, 17, 0, 566, 64, 174, 576, 10, 0, 626, 4, 170

Offset

1,5

Links

Table of n, a(n) for n=1..76.

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A001822, A363902.

Cf. A103638, A363976.

Sequence in context: A277531 A284982 A089962 * A127155 A211793 A145880

Adjacent sequences: A363968 A363969 A363970 * A363972 A363973 A363974

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 30 2023

Status

approved