A276485 Numerator of Sum_{k=1..n} 1/k^n.

1, 5, 251, 22369, 806108207, 47464376609, 774879868932307123, 248886558707571775009601, 4106541588424891370931874221019, 413520574906423083987893722912609, 7429165883912264897181708263009894640627544300697

Offset: 1

Author

Ilya Gutkovskiy, Sep 05 2016

Keywords

• nonn
• frac

Comments

Also numerators 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) = 251, 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, A276487 (denominators).

Programs

Mathematica

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

PARI

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