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A103347
Numerators of Sum_{k=1..n} 1/k^7 = Zeta(7,n).
6
1, 129, 282251, 36130315, 2822716691183, 940908897061, 774879868932307123, 99184670126682733619, 650750755630450535274259, 650750820166709327386387, 12681293156341501091194786541177, 12681293507322704937269896541177
OFFSET
1,2
COMMENTS
a(n) gives the partial sums, Zeta(7,n), of Euler's Zeta(7). 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 A103348 and for the rationals Zeta(7,n) see the W. Lang link under A103345.
LINKS
FORMULA
a(n) = numerator(sum_{k=1..n} 1/k^7).
G.f. for rationals Zeta(7, n): polylogarithm(7, x)/(1-x).
MAPLE
f:= n -> numer(Psi(6, n+1)/720 + Zeta(7)):
map(f, [$1..20]); # Robert Israel, Mar 28 2018
MATHEMATICA
s=0; lst={}; Do[s+=n^1/n^8; AppendTo[lst, Numerator[s]], {n, 3*4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 24 2009 *)
Table[ HarmonicNumber[n, 7] // Numerator, {n, 1, 12}] (* Jean-François Alcover, Dec 04 2013 *)
KEYWORD
nonn,frac,easy
AUTHOR
Wolfdieter Lang, Feb 15 2005
STATUS
approved