A276487 - OEIS

%I #16 Sep 20 2016 13:15:35

%S 1,4,216,20736,777600000,46656000000,768464444160000000,

%T 247875891108249600000000,4098310578334288576512000000000,

%U 413109706296096288512409600000000,7425496288284402957501110551810198732800000000000

%N Denominator of Sum_{k=1..n} 1/k^n.

%C Also denominator of zeta(n) - Hurwitz zeta(n,n+1), where zeta(s) is the Riemann zeta function and Hurwitz zeta(s,a) is the Hurwitz zeta function.

%C Sum_{k>=1} 1/k^n = zeta(n).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RiemannZetaFunction.html">Riemann Zeta Function</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HurwitzZetaFunction.html">Hurwitz Zeta Function</a>

%e 1, 5/4, 251/216, 22369/20736, 806108207/777600000, 47464376609/46656000000, 774879868932307123/768464444160000000, ...

%e a(3) = 216, because 1/1^3 + 1/2^3 + 1/3^3 = 251/216.

%p A276487:=n->denom(add(1/k^n, k=1..n)): seq(A276487(n), n=1..12); # _Wesley Ivan Hurt_, Sep 07 2016

%t Table[Denominator[HarmonicNumber[n, n]], {n, 1, 11}]

%o (PARI) a(n) = denominator(sum(k=1, n, 1/k^n)); \\ _Michel Marcus_, Sep 06 2016

%Y Cf. A001008, A002805, A007406, A007407, A031971, A276485 (numerators).

%K nonn,frac

%O 1,2

%A _Ilya Gutkovskiy_, Sep 05 2016