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%I #22 Jul 11 2020 02:32:33
%S 1,64,46656,2985984,46656000000,46656000000,5489031744000000,
%T 351298031616000000,256096265048064000000,51219253009612800000,
%U 90738031080962661580800000,90738031080962661580800000
%N Denominators of Sum_{k=1..n} 1/k^6 = Zeta(6,n).
%C For the numerators and comments, see A103345.
%F a(n) = denominator(Sum_{k=1..n} 1/k^6) = denominator(A291456(n)/(n!)^6). - _Petros Hadjicostas_, May 10 2020
%e The first few fractions are 1, 65/64, 47449/46656, 3037465/2985984, 47463376609/46656000000, ... = A103345/A103346. - _Petros Hadjicostas_, May 10 2020
%t s=0; lst={}; Do[s+=n^1/n^7; AppendTo[lst,Denominator[s]],{n,3*4!}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Jan 24 2009 *)
%t Table[ HarmonicNumber[n, 6] // Denominator, {n, 1, 12}] (* _Jean-François Alcover_, Dec 04 2013 *)
%Y Cf. A103345, A291456.
%K nonn,frac,easy
%O 1,2
%A _Wolfdieter Lang_, Feb 15 2005