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A136676
Numerator of Sum_{k=1..n} (-1)^(k+1)/k^5.
10
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
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
KEYWORD
frac,nonn
AUTHOR
Alexander Adamchuk, Jan 16 2008
STATUS
approved