A276487 Denominator of Sum_{k=1..n} 1/k^n.

1, 4, 216, 20736, 777600000, 46656000000, 768464444160000000, 247875891108249600000000, 4098310578334288576512000000000, 413109706296096288512409600000000, 7425496288284402957501110551810198732800000000000

Offset: 1

Author

Ilya Gutkovskiy, Sep 05 2016

Keywords

• nonn
• frac

Comments

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.

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

Examples

			1, 5/4, 251/216, 22369/20736, 806108207/777600000, 47464376609/46656000000, 774879868932307123/768464444160000000, ...
a(3) = 216, because 1/1^3 + 1/2^3 + 1/3^3 = 251/216.
		

Links

• Eric Weisstein's World of Mathematics, Harmonic Number
• Eric Weisstein's World of Mathematics, Riemann Zeta Function
• Eric Weisstein's World of Mathematics, Hurwitz Zeta Function

Crossrefs

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

Programs

Maple

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

Mathematica

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

PARI

a(n) = denominator(sum(k=1, n, 1/k^n)); \\ Michel Marcus, Sep 06 2016