Search: id:A007410
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%I A007410 M5050
%S A007410 1,17,1393,22369,14001361,14011361,33654237761,538589354801,
%T A007410 43631884298881,43635917056897,638913789210188977,638942263173398977,
%U A007410 18249420414596570742097,18249859383918836502097,18250192489014819937873
%N A007410 Numerator of Sum k^(-4); k = 1..n.
%C A007410 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
%C A007410 p^2 divides a(p-1) for prime p = 37. - Alexander Adamchuk (alex(AT)kolmogorov.com), 
               Nov 07 2006
%C A007410 Denominators are A007480. See the W. Lang link under A103345 for the 
               rationals and more.
%C A007410 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.
%D A007410 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.
%D A007410 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A007410 T. D. Noe, <a href="b007410.txt">Table of n, a(n) for n=1..200</a>
%H A007410 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha103.htm">Factorizations of many number sequences</a>
%H A007410 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha1297.htm">Factorizations of many number sequences</a>
%t A007410 Numerator[Table[Sum[1/k^4,{k,1,n}],{n,1,20}]] - Alexander Adamchuk (alex(AT)kolmogorov.com), 
               Jul 07 2006
%Y A007410 Cf. A001008, A007406, A007408, A007480.
%Y A007410 Sequence in context: A022546 A128542 A067409 this_sequence A072160 A078814 
               A129911
%Y A007410 Adjacent sequences: A007407 A007408 A007409 this_sequence A007411 A007412 
               A007413
%K A007410 nonn,frac
%O A007410 1,2
%A A007410 N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein

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