A034680 Sum of sixth powers of unitary divisors.

1, 65, 730, 4097, 15626, 47450, 117650, 262145, 531442, 1015690, 1771562, 2990810, 4826810, 7647250, 11406980, 16777217, 24137570, 34543730, 47045882, 64019722, 85884500, 115151530, 148035890, 191365850, 244140626, 313742650

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

Dirichlet g.f.: zeta(s)*zeta(s-6)/zeta(2s-6). - R. J. Mathar, Apr 12 2011

If n = Product (p_j^k_j) then a(n) = Product (1 + p_j^(6*k_j)). - Ilya Gutkovskiy, Nov 04 2018

Sum_{k=1..n} a(k) ~ 1350*Zeta(7)*n^7 / Pi^8. - Vaclav Kotesovec, Feb 07 2019

Mathematica

Total[#^6]&/@Table[Select[Divisors[n], GCD[#, n/#]==1&], {n, 30}] (* Harvey P. Dale, Jul 17 2011 *)
a[1] = 1; a[n_] := Times @@ (1 + First[#]^(6*Last[#]) & /@ FactorInteger[n]); s = Array[a, 50] (* Amiram Eldar, Aug 10 2019 *)

Crossrefs

Cf. A034444, A034448.

Row n=6 of A286880.

Sequence in context: A351269 A088677 A321562 * A351301 A017675 A013954

Adjacent sequences: A034677 A034678 A034679 * A034681 A034682 A034683

Keyword

nonn,mult

Author

Erich Friedman

Status

approved