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

Author

Alexander Adamchuk, Jan 16 2008

Keywords

• frac
• nonn

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

Examples

			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
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..382
• Eric Weisstein's World of Mathematics, Harmonic Number.

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).

Programs

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 *)