A136676 Numerator of Sum_{k=1..n} (-1)^(k+1)/k^5.

1, 31, 7565, 241837, 755989457, 755889457, 12705011703799, 406547611705943, 98792790681344149, 98791774426324117, 15910615688635928566967, 15910549913780913466967, 5907492176026179821253778331

Offset

1,2

Comments

a(n) is prime for n in A136685.

Lim_{n -> infinity} a(n)/A334604(n) = A267316 = (15/16)*A013663. - Petros Hadjicostas, May 07 2020

Links

Table of n, a(n) for n=1..13.

Eric Weisstein's World of Mathematics, Harmonic Number.

Example

The first few fractions are 1, 31/32, 7565/7776, 241837/248832, 755989457/777600000, 755889457/777600000, ... = a(n)/A334604(n). - Petros Hadjicostas, May 07 2020

Mathematica

Table[ Numerator[ Sum[ (-1)^(k+1)/k^5, {k, 1, n} ] ], {n, 1, 30} ]

Prog

(PARI) a(n) = numerator(sum(k=1, n, (-1)^(k+1)/k^5)); \\ Michel Marcus, May 07 2020

Crossrefs

Cf. A001008, A007406, A007408, A007410, A013663, A058313, A099828, A103345, A119682, A120296, A136675, A136677, A136681, A136682, A136683, A136684, A136685, A136686, A267316, A334604 (denominators).

Sequence in context: A212858 A337678 A059384 * A135811 A119598 A139295

Adjacent sequences: A136673 A136674 A136675 * A136677 A136678 A136679

Keyword

frac,nonn

Author

Alexander Adamchuk, Jan 16 2008

Status

approved