A099828 Numerator of the generalized harmonic number H(n,5) = Sum_{k=1..n} 1/k^5.
1, 33, 8051, 257875, 806108207, 268736069, 4516906311683, 144545256245731, 105375212839937899, 105376229094957931, 16971048697474072945481, 16971114472329088045481, 6301272372663207205033976933
Offset: 1
Examples
H(n,5) = {1, 33/32, 8051/7776, 257875/248832, ... } = A099828/A069052. For example, a(2) = numerator(1 + 1/2^5) = numerator(33/32) = 33 and a(3) = numerator(1 + 1/2^5 + 1/3^5) = numerator(8051/7776) = 8051. [Edited by _Petros Hadjicostas_, May 10 2020]
Links
- Alexander Adamchuk, Nov 07 2006, Table of n, a(n) for n = 1..100
- Wolfdieter Lang, Rational Zeta(k,n) and more.
- Eric Weisstein's World of Mathematics, Wolstenholme's Theorem.
Crossrefs
Programs
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Mathematica
Numerator[Table[Sum[1/k^5, {k, 1, n}], {n, 1, 20}]] Numerator[Table[HarmonicNumber[n, 5], {n, 1, 20}]] Table[Numerator[Sum[1/k^5,{k,1,n}]],{n,1,100}] (* Alexander Adamchuk, Nov 07 2006 *)
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PARI
a(n) = numerator(sum(k=1, n, 1/k^5)); \\ Michel Marcus, May 10 2020
Formula
a(n) = numerator(Sum_{k=1..n} 1/k^5) = numerator(HarmonicNumber[n, 5]).
Comments