A069052 Denominator of Sum_{i = 1..n} 1/i^5.

1, 32, 7776, 248832, 777600000, 259200000, 4356374400000, 139403980800000, 101625502003200000, 101625502003200000, 16366888723117363200000, 16366888723117363200000, 6076911214672415134617600000

Offset: 1

Author

Benoit Cloitre, Apr 03 2002

Keywords

• easy
• frac
• nonn

Comments

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).

Examples

			The first few fractions are 1, 33/32, 8051/7776, 257875/248832, ... = A099828/A069052. - _Petros Hadjicostas_, May 10 2020
		

Links

• Wolfdieter Lang, Rational Zeta(k,n) and more.

Crossrefs

Numerators are A099828.

Cf. A002805, A007480, A099827.

Programs

Mathematica

s = 0; lst = {}; Do[s += 1/n^5; AppendTo[lst, Denominator[s]], {n, 3 * 4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 24 2009 *)
Denominator[Table[Sum[1/i^5, {i, n}], {n, 20}]] (* Alonso del Arte, May 10 2020 *)

Formula

a(n) = denominator(Sum_{k=1..n} 1/k^5) = denominator(A099827(n)/(n!)^5). - Petros Hadjicostas, May 10 2020