A103346 Denominators of Sum_{k=1..n} 1/k^6 = Zeta(6,n).

1, 64, 46656, 2985984, 46656000000, 46656000000, 5489031744000000, 351298031616000000, 256096265048064000000, 51219253009612800000, 90738031080962661580800000, 90738031080962661580800000

Offset: 1

Author

Wolfdieter Lang, Feb 15 2005

Keywords

• nonn
• frac
• easy

Comments

For the numerators and comments, see A103345.

Examples

			The first few fractions are 1, 65/64, 47449/46656, 3037465/2985984, 47463376609/46656000000, ... = A103345/A103346. - _Petros Hadjicostas_, May 10 2020
		

Crossrefs

Cf. A103345, A291456.

Programs

Mathematica

s=0; lst={}; Do[s+=n^1/n^7; AppendTo[lst,Denominator[s]],{n,3*4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 24 2009 *)
Table[ HarmonicNumber[n, 6] // Denominator, {n, 1, 12}] (* Jean-François Alcover, Dec 04 2013 *)

Formula

a(n) = denominator(Sum_{k=1..n} 1/k^6) = denominator(A291456(n)/(n!)^6). - Petros Hadjicostas, May 10 2020