A136675 Numerator of Sum_{k=1..n} (-1)^(k+1)/k^3.

1, 7, 197, 1549, 195353, 194353, 66879079, 533875007, 14436577189, 14420574181, 19209787242911, 19197460851911, 42198121495296467, 6025866788581781, 6027847576222613, 48209723660000029, 236907853607882606477

Offset: 1

Author

Alexander Adamchuk, Jan 16 2008

Keywords

• frac
• nonn

Comments

a(n) is prime for n in A136683.

Lim_{n -> infinity} a(n)/A334582(n) = A197070. - Petros Hadjicostas, May 07 2020

Examples

			The first few fractions are 1, 7/8, 197/216, 1549/1728, 195353/216000, 194353/216000, 66879079/74088000, 533875007/592704000, ... = a(n)/A334582(n). - _Petros Hadjicostas_, May 06 2020
		

Links

• Robert Israel, Table of n, a(n) for n = 1..768
• Eric Weisstein's World of Mathematics, Harmonic Number.
• Wikipedia, Dirichlet eta function.

Crossrefs

Cf. A001008, A007406, A007408, A007410, A058313, A099828, A103345, A119682, A120296, A136676, A136677, A136681, A136682, A136683, A136684, A136685, A136686, A197070, A334582 (denominators).

Programs

Maple

map(numer,ListTools:-PartialSums([seq((-1)^(k+1)/k^3, k=1..100)])); # Robert Israel, Nov 09 2023

Mathematica

(* Program #1 *) Table[Numerator[Sum[(-1)^(k+1)/k^3, {k,1,n}]], {n,1,50}]
(* Program #2 *) Numerator[Accumulate[Table[(-1)^(k+1) 1/k^3, {k,50}]]] (* Harvey P. Dale, Feb 12 2013 *)

PARI

a(n) = numerator(sum(k=1, n, (-1)^(k+1)/k^3)); \\ Michel Marcus, May 07 2020