A386786 a(n) = n^4*sigma_6(n).

0, 1, 1040, 59130, 1065216, 9766250, 61495200, 282477650, 1090785280, 3491573931, 10156900000, 25937439242, 62986222080, 137858520410, 293776756000, 577478362500, 1116964192256, 2015993983970, 3631236888240, 6131066388122, 10403165760000, 16702903444500, 26974936811680

Offset

0,3

Links

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

Formula

G.f.: Sum_{k>=1} k^4*x^k*(1 + 1013*x^k + 47840*x^(2*k) + 455192*x^(3*k) + 1310354*x^(4*k) + 1310354*x^(5*k) + 455192*x^(6*k) + 47840*x^(7*k) + 1013*x^(8*k) + x^(9*k))/(1 - x^k)^11.

a(n) = n^4*A013954(n).

Dirichlet g.f.: zeta(s-4)*zeta(s-10). - R. J. Mathar, Aug 03 2025

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

Mathematica

Table[n^4*DivisorSigma[6, n], {n, 0, 30}]
nmax = 30; CoefficientList[Series[Sum[k^4*x^k*(1 + 1013*x^k + 47840*x^(2*k) + 455192*x^(3*k) + 1310354*x^(4*k) + 1310354*x^(5*k) + 455192*x^(6*k) + 47840*x^(7*k) + 1013*x^(8*k) + x^(9*k))/(1 - x^k)^11, {k, 1, nmax}], {x, 0, nmax}], x]

Prog

(Magma) [0] cat [n^4*DivisorSigma(6, n): n in [1..35]]; // Vincenzo Librandi, Aug 03 2025

Crossrefs

Cf. A280022, A386783, A280025, A386784, A386785, A386787, A386788.

Cf. A013665, A013954, A386750, A386777, A386780.

Sequence in context: A069456 A210259 A233854 * A168412 A183742 A252618

Adjacent sequences: A386783 A386784 A386785 * A386787 A386788 A386789

Keyword

nonn,mult,easy

Author

Vaclav Kotesovec, Aug 02 2025

Status

approved