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

Author

Erich Friedman

Keywords

• nonn
• mult

Links

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

Crossrefs

Cf. A034444, A034448.

Row n=6 of A286880.

Programs

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 *)

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