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A103349 Numerators of sum_{k=1..n} 1/k^8 = Zeta(8,n). 4
1, 257, 1686433, 431733409, 168646292872321, 168646392872321, 972213062238348973121, 248886558707571775009601, 1632944749460578249437992161, 1632944765723715465050248417 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) gives the partial sums, Zeta(8,n) of Euler's Zeta(8). Zeta(k,n) is also called H(k,n) because for k=1 these are the harmonic numbers H(n) A001008/A002805.

For the denominators see A103350 and for the rationals Zeta(8,n) see the W. Lang link under A103345.

LINKS

Table of n, a(n) for n=1..10.

FORMULA

a(n)=numerator(sum_{k=1..n} 1/k^8).

G.f. for rationals Zeta(8, n): polylogarithm(8, x)/(1-x).

MATHEMATICA

s=0; lst={}; Do[s+=n^1/n^9; AppendTo[lst, Numerator[s]], {n, 3*4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 24 2009 *)

Table[ HarmonicNumber[n, 8] // Numerator, {n, 1, 10}] (* Jean-Fran├žois Alcover, Dec 04 2013 *)

CROSSREFS

For k=1..7 see: A001008/A002805, A007406/A007407, A007408/A007409, A007410/A007480, A099828/A069052, A103345/A103346, A103347/A103348.

Sequence in context: A218723 A097736 A283510 * A291506 A275098 A194155

Adjacent sequences:  A103346 A103347 A103348 * A103350 A103351 A103352

KEYWORD

nonn,frac,easy

AUTHOR

Wolfdieter Lang, Feb 15 2005

STATUS

approved

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Last modified November 29 05:05 EST 2021. Contains 349416 sequences. (Running on oeis4.)