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A007410
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Numerator of Sum_{k=1..4} k^(-4).
(Formerly M5050)
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34
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1, 17, 1393, 22369, 14001361, 14011361, 33654237761, 538589354801, 43631884298881, 43635917056897, 638913789210188977, 638942263173398977, 18249420414596570742097, 18249859383918836502097, 18250192489014819937873
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OFFSET
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1,2
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COMMENTS
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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
Denominators are A007480. See the W. Lang link under A103345 for the rationals and more.
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.
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REFERENCES
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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).
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LINKS
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FORMULA
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Numerators of the coefficients in the expansion of PolyLog(4, x)/(1 - x). - Ilya Gutkovskiy, Apr 10 2017
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MATHEMATICA
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Accumulate[1/Range[20]^4]//Numerator (* Harvey P. Dale, Jun 28 2020 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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