A136677 Numerator of Sum_{k=1..n} (-1)^(k+1)/k^6.

1, 63, 45991, 2942695, 45982595359, 5109066151, 601081707598999, 38469080386820311, 252396118308232060471, 252395862211967012407, 447134922152359540530757327, 447134770212444455649757327, 2158234586764514215343657417779543, 308319185132349039219686748825649

Offset

1,2

Comments

p divides a(p-1) for prime p > 2. a(n) is prime for n = {19, 47, 164, ...} = A136686.

Lim_{n -> infinity} a(n)/A334605(n) = A275703 = (31/32)*A013664. - Petros Hadjicostas, May 07 2020

Links

Harvey P. Dale, Table of n, a(n) for n = 1..382

Eric Weisstein's World of Mathematics, Harmonic Number.

Example

The first few fractions are 1, 63/64, 45991/46656, 2942695/2985984, 45982595359/46656000000, 5109066151/5184000000, ... = a(n)/A334605(n). - Petros Hadjicostas, May 07 2020

Mathematica

Table[ Numerator[ Sum[ (-1)^(k+1)/k^6, {k, 1, n} ] ], {n, 1, 30} ]
Accumulate[Table[(-1)^(k+1)/k^6, {k, 20}]]//Numerator (* Harvey P. Dale, Aug 21 2023 *)

Crossrefs

Cf. A013664, A058313, A119682, A120296, A136675, A136676.

Cf. A001008, A007406, A007408, A007410, A099828, A103345, A275703.

Cf. A136681, A136682, A136683, A136684, A136685, A136686, A334605 (denominators).

Sequence in context: A110852 A212859 A239672 * A135812 A069452 A229846

Adjacent sequences: A136674 A136675 A136676 * A136678 A136679 A136680

Keyword

frac,nonn

Author

Alexander Adamchuk, Jan 16 2008

Status

approved