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

1,2

Comments

a(n) is prime for n in A136683.

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A128786 A034835 A041371 * A099198 A365988 A058391

Adjacent sequences: A136672 A136673 A136674 * A136676 A136677 A136678

Keyword

frac,nonn

Author

Alexander Adamchuk, Jan 16 2008

Status

approved