A386783 a(n) = n^4*sigma_2(n).

0, 1, 80, 810, 5376, 16250, 64800, 120050, 348160, 597051, 1300000, 1786202, 4354560, 4855370, 9604000, 13162500, 22347776, 24221090, 47764080, 47176202, 87360000, 97240500, 142896160, 148315730, 282009600, 254296875, 388429600, 435781620, 645388800, 595530602, 1053000000

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 + 57*x^k + 302*x^(2*k) + 302*x^(3*k) + 57*x^(4*k) + x^(5*k)) / (1 - x^k)^7.

a(n) = n^4*A001157(n).

Dirichlet g.f.: zeta(s-4)*zeta(s-6). - R. J. Mathar, Aug 03 2025

Sum_{k=0..n} a(k) ~ zeta(3) * n^7 / 7. - Amiram Eldar, Nov 11 2025

Mathematica

Table[n^4*DivisorSigma[2, n], {n, 0, 40}]
nmax = 40; CoefficientList[Series[Sum[k^4*x^k*(1 + 57*x^k + 302*x^(2*k) + 302*x^(3*k) + 57*x^(4*k) + x^(5*k)) / (1 - x^k)^7, {k, 1, nmax}], {x, 0, nmax}], x]

Prog

(Magma) [0] cat [n^4*DivisorSigma(2, n): n in [1..35]]; // Vincenzo Librandi, Aug 03 2025

Crossrefs

Cf. A280022, A280025, A386784, A386785, A386786, A386787, A386788.

Cf. A001157, A002117, A328259, A386745, A386746.

Sequence in context: A279745 A062911 A024392 * A200550 A052519 A246545

Adjacent sequences: A386780 A386781 A386782 * A386784 A386785 A386786

Keyword

nonn,mult,easy

Author

Vaclav Kotesovec, Aug 02 2025

Status

approved