A386747 a(n) = n^2*sigma_4(n).

0, 1, 68, 738, 4368, 15650, 50184, 117698, 279616, 538083, 1064200, 1771682, 3223584, 4826978, 8003464, 11549700, 17895680, 24137858, 36589644, 47046242, 68359200, 86861124, 120474376, 148036418, 206356608, 244531875, 328234504, 392263236, 514104864, 594824162

Offset

0,3

Links

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

Formula

G.f.: Sum_{k>=1} k^6*x^k*(1 + x^k)/(1 - x^k)^3. - Amiram Eldar, Aug 01 2025

a(n) = n^2*A001159(n).

Dirichlet g.f.: zeta(s-2)*zeta(s-6).- R. J. Mathar, Aug 03 2025

Sum_{k=0..n} a(k) ~ zeta(5) * n^7 / 7. - Amiram Eldar, Nov 11 2025

Mathematica

Table[n^2*DivisorSigma[4, n], {n, 0, 40}]
nmax = 40; CoefficientList[Series[Sum[k^6*x^k*(1 + x^k)/(1 - x^k)^3, {k, 1, nmax}], {x, 0, nmax}], x]

Prog

(Magma) [0] cat [n^2*DivisorSigma(4, n): n in [1..35]]; // Vincenzo Librandi, Aug 02 2025

Crossrefs

Cf. A000290, A001159, A013663, A386749, A386748.

Sequence in context: A244440 A166398 A200876 * A039507 A250144 A250338

Adjacent sequences: A386744 A386745 A386746 * A386748 A386749 A386750

Keyword

nonn,mult,easy

Author

Vaclav Kotesovec, Aug 01 2025

Status

approved