A386750 a(n) = n*sigma_6(n).

0, 1, 130, 2190, 16644, 78130, 284700, 823550, 2130440, 4789539, 10156900, 19487182, 36450360, 62748530, 107061500, 171104700, 272696336, 410338690, 622640070, 893871758, 1300395720, 1803574500, 2533333660, 3404825470, 4665663600, 6103906275, 8157308900, 10474721820

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..3000

Formula

G.f.: Sum_{k>=1} k^7*x^(k-1)/(1 - x^k)^2.

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

Dirichlet g.f.: zeta(s-1)*zeta(s-7). - R. J. Mathar, Aug 03 2025

Sum_{k=0..n} a(k) ~ zeta(7) * n^8 / 8. - Amiram Eldar, Nov 11 2025

Mathematica

Table[n*DivisorSigma[6, n], {n, 0, 40}]
nmax = 40; CoefficientList[Series[x*Sum[k^7*x^(k-1)/(1 - x^k)^2, {k, 1, nmax}], {x, 0, nmax}], x]

Prog

(Magma) [0] cat [n*DivisorSigma(6, n): n in [1..25]]; // Vincenzo Librandi, Aug 02 2025

Crossrefs

Cf. A013665, A013954.

Cf. A064987, A328259, A281372, A386749, A282050, A282060, A386751.

Sequence in context: A278658 A254924 A185584 * A301545 A229329 A262108

Adjacent sequences: A386747 A386748 A386749 * A386751 A386752 A386753

Keyword

nonn,mult,easy

Author

Vaclav Kotesovec, Aug 01 2025

Status

approved