

A103346


Denominators of Sum_{k=1..n} 1/k^6 = Zeta(6,n).


8



1, 64, 46656, 2985984, 46656000000, 46656000000, 5489031744000000, 351298031616000000, 256096265048064000000, 51219253009612800000, 90738031080962661580800000, 90738031080962661580800000
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OFFSET

1,2


COMMENTS

For the numerators and comments, see A103345.


LINKS

Table of n, a(n) for n=1..12.


FORMULA

a(n) = denominator(Sum_{k=1..n} 1/k^6) = denominator(A291456(n)/(n!)^6).  Petros Hadjicostas, May 10 2020


EXAMPLE

The first few fractions are 1, 65/64, 47449/46656, 3037465/2985984, 47463376609/46656000000, ... = A103345/A103346.  Petros Hadjicostas, May 10 2020


MATHEMATICA

s=0; lst={}; Do[s+=n^1/n^7; AppendTo[lst, Denominator[s]], {n, 3*4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 24 2009 *)
Table[ HarmonicNumber[n, 6] // Denominator, {n, 1, 12}] (* JeanFrançois Alcover, Dec 04 2013 *)


CROSSREFS

Cf. A103345, A291456.
Sequence in context: A016830 A249076 A334605 * A123394 A069445 A227604
Adjacent sequences: A103343 A103344 A103345 * A103347 A103348 A103349


KEYWORD

nonn,frac,easy


AUTHOR

Wolfdieter Lang, Feb 15 2005


STATUS

approved



