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Search: id:A007410
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| A007410 |
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Numerator of Sum k^(-4); k = 1..n.
(Formerly M5050)
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+0
33
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| 1, 17, 1393, 22369, 14001361, 14011361, 33654237761, 538589354801, 43631884298881, 43635917056897, 638913789210188977, 638942263173398977, 18249420414596570742097, 18249859383918836502097, 18250192489014819937873
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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 (alex(AT)kolmogorov.com), Jul 07 2006
p^2 divides a(p-1) for prime p = 37. - Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 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[1/k^4,{k,1,n}] for n->infinity is (Pi^4)/90 which is approximately 1.082323234.
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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 of 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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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
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MATHEMATICA
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Numerator[Table[Sum[1/k^4, {k, 1, n}], {n, 1, 20}]] - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 07 2006
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CROSSREFS
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Cf. A001008, A007406, A007408, A007480.
Sequence in context: A022546 A128542 A067409 this_sequence A072160 A078814 A129911
Adjacent sequences: A007407 A007408 A007409 this_sequence A007411 A007412 A007413
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KEYWORD
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nonn,frac
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein
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