A386778 a(n) = n^2*sigma_8(n).

0, 1, 1028, 59058, 1052688, 9765650, 60711624, 282475298, 1077952576, 3487315923, 10039088200, 25937424722, 62169647904, 137858492018, 290384606344, 576739757700, 1103823438080, 2015993900738, 3584960768844, 6131066258162, 10280182567200, 16682426149284, 26663672614216

Offset

0,3

Links

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

Formula

G.f.: Sum_{k>=1} k^10*x^k*(1 + x^k)/(1 - x^k)^3.

a(n) = n^2*A013956(n).

Dirichlet g.f.: zeta(s-2)*zeta(s-10). - R. J. Mathar, Aug 03 2025

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

Mathematica

Table[n^2*DivisorSigma[8, n], {n, 0, 30}]
nmax = 30; CoefficientList[Series[Sum[k^10*x^k*(1 + x^k)/(1 - x^k)^3, {k, 1, nmax}], {x, 0, nmax}], x]

Prog

(Magma) [0] cat [n^2*DivisorSigma(8, n): n in [1..35]]; // Vincenzo Librandi, Aug 04 2025

Crossrefs

Cf. A282097, A386745, A282099, A386747, A282751, A386777, A282753.

Cf. A013667, A013956, A386751.

Sequence in context: A066133 A119455 A252772 * A168189 A383917 A045031

Adjacent sequences: A386775 A386776 A386777 * A386779 A386780 A386781

Keyword

nonn,mult,easy

Author

Vaclav Kotesovec, Aug 02 2025

Status

approved