A386777 a(n) = n^2*sigma_6(n).

0, 1, 260, 6570, 66576, 390650, 1708200, 5764850, 17043520, 43105851, 101569000, 214359002, 437404320, 815730890, 1498861000, 2566570500, 4363141376, 6975757730, 11207521260, 16983563402, 26007914400, 37875064500, 55733340520, 78310985810, 111975926400, 152597656875

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Formula

G.f.: Sum_{k>=1} k^8*x^k*(1 + x^k)/(1 - x^k)^3.

a(n) = n^2*A013954(n).

Dirichlet g.f.: zeta(s-2)*zeta(s-8). - R. J. Mathar, Aug 03 2025

Sum_{k=0..n} a(k) ~ zeta(7) * n^9 / 9. - Amiram Eldar, Nov 11 2025

Mathematica

Table[n^2*DivisorSigma[6, n], {n, 0, 30}]
nmax = 30; CoefficientList[Series[Sum[k^8*x^k*(1 + x^k)/(1 - x^k)^3, {k, 1, nmax}], {x, 0, nmax}], x]

Prog

(Magma) [0] cat [n^2*DivisorSigma(6, n): n in [1..35]]; // Vincenzo Librandi, Aug 04 2025

Crossrefs

Cf. A282097, A386745, A282099, A386747, A282751, A282753, A386778.

Cf. A013665, A013954, A386750.

Sequence in context: A287923 A238029 A264254 * A254647 A168187 A067639

Adjacent sequences: A386774 A386775 A386776 * A386778 A386779 A386780

Keyword

nonn,mult,easy

Author

Vaclav Kotesovec, Aug 02 2025

Status

approved