A386749 a(n) = n*sigma_4(n).

0, 1, 34, 246, 1092, 3130, 8364, 16814, 34952, 59787, 106420, 161062, 268632, 371306, 571676, 769980, 1118480, 1419874, 2032758, 2476118, 3417960, 4136244, 5476108, 6436366, 8598192, 9781275, 12624404, 14528268, 18360888, 20511178, 26179320, 28629182, 35791392, 39621252

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..9000

Formula

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

a(n) = n*A001159(n).

Dirichlet g.f.: zeta(s-1)*zeta(s-5). - R. J. Mathar, Aug 03 2025

Sum_{k=0..n} a(k) ~ zeta(5) * n^6 / 6. - Amiram Eldar, Nov 11 2025

Mathematica

Table[n*DivisorSigma[4, n], {n, 0, 50}]
nmax = 50; CoefficientList[Series[x*Sum[k^5*x^(k-1)/(1 - x^k)^2, {k, 1, nmax}], {x, 0, nmax}], x]

Prog

(Magma) [0] cat [n*DivisorSigma(4, n): n in [1..35]]; // Vincenzo Librandi, Aug 02 2025
(PARI) a(n) = if (n, n*sigma(n, 4), 0); \\ Michel Marcus, Aug 02 2025

Crossrefs

Cf. A064987, A328259, A281372, A282050, A386750, A282060, A386751.

Cf. A001159, A013663, A386747, A386748.

Sequence in context: A233300 A281052 A020872 * A302474 A183319 A190422

Adjacent sequences: A386746 A386747 A386748 * A386750 A386751 A386752

Keyword

nonn,mult,easy

Author

Vaclav Kotesovec, Aug 01 2025

Status

approved