OFFSET
1,2
COMMENTS
p divides a(p-1) for prime p > 5. p divides a((p-1)/2) for prime p > 5. p^2 divides a((p-1)/2) for prime p = 31, 37. - Alexander Adamchuk, Jul 07 2006
p^2 divides a(p-1) for prime p = 37. - Alexander Adamchuk, Nov 07 2006
The limit of the rationals Zeta(n) := Sum_{k=1..n} 1/k^4 as n -> infinity is (Pi^4)/90, which is approximately 1.082323234. See A013662.
REFERENCES
D. Y. Savio, E. A. Lamagna, and S.-M. Liu, Summation of harmonic numbers, pp. 12-20, in: E. Kaltofen and S. M. Watt, editors, Computers and Mathematics, Springer-Verlag, NY, 1989.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. D. Noe, Table of n, a(n) for n=1..200
Hisanori Mishima, Factorizations of many number sequences.
Hisanori Mishima, Factorizations of many number sequences.
FORMULA
Numerators of the coefficients in the expansion of PolyLog(4, x)/(1 - x). - Ilya Gutkovskiy, Apr 10 2017
MATHEMATICA
Numerator[Table[Sum[1/k^4, {k, 1, n}], {n, 1, 20}]] (* Alexander Adamchuk, Jul 07 2006 *)
Accumulate[1/Range[20]^4]//Numerator (* Harvey P. Dale, Jun 28 2020 *)
PROG
(PARI) a(n)=numerator(sum(k=1, n, 1/k^4)) \\ Charles R Greathouse IV, Jul 19 2011
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
STATUS
approved