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%I #31 May 10 2020 19:29:17
%S 1,32,7776,248832,777600000,259200000,4356374400000,139403980800000,
%T 101625502003200000,101625502003200000,16366888723117363200000,
%U 16366888723117363200000,6076911214672415134617600000
%N Denominator of Sum_{i = 1..n} 1/i^5.
%C If 1 <= n <= 19, a(n) = A007480(n) * A002805(n) = denominator(Sum_{i = 1..n} 1/i^4) * denominator(Sum_{i = 1..n} 1/i).
%H Wolfdieter Lang, <a href="/A103345/a103345.pdf">Rational Zeta(k,n) and more</a>.
%F a(n) = denominator(Sum_{k=1..n} 1/k^5) = denominator(A099827(n)/(n!)^5). - _Petros Hadjicostas_, May 10 2020
%e The first few fractions are 1, 33/32, 8051/7776, 257875/248832, ... = A099828/A069052. - _Petros Hadjicostas_, May 10 2020
%t s = 0; lst = {}; Do[s += 1/n^5; AppendTo[lst, Denominator[s]], {n, 3 * 4!}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Jan 24 2009 *)
%t Denominator[Table[Sum[1/i^5, {i, n}], {n, 20}]] (* _Alonso del Arte_, May 10 2020 *)
%Y Numerators are A099828.
%Y Cf. A002805, A007480, A099827.
%K easy,frac,nonn
%O 1,2
%A _Benoit Cloitre_, Apr 03 2002