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A034680 Sum of sixth powers of unitary divisors. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A268265 A088677 A321562 * A017675 A013954 A294301

Adjacent sequences:  A034677 A034678 A034679 * A034681 A034682 A034683

KEYWORD

nonn,mult

AUTHOR

Erich Friedman

STATUS

approved

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Last modified November 19 20:42 EST 2019. Contains 329323 sequences. (Running on oeis4.)