%I A007408 M4670
%S A007408 1,9,251,2035,256103,28567,9822481,78708473,19148110939,19164113947,
%T A007408 25523438671457,25535765062457,56123375845866029,56140429821090029,
%U A007408 56154295334575853,449325761325072949,2207911834254200646437
%N A007408 Wolstenholme numbers: numerator of Sum_{k=1..n} 1/k^3.
%C A007408 By Theorem 131 in Hardy and Wright, p^2 divides a(p-1) for prime p > 
               5. - T. D. Noe (noe(AT)sspectra.com), Sep 05 2002
%C A007408 p^3 divides a(p-1) for prime p = 37. Primes p such that p divides a((p+1)/
               2) are listed in A124787(n) = {3, 11, 17, 89}. - Alexander Adamchuk 
               (alex(AT)kolmogorov.com), Nov 07 2006
%D A007408 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A007408 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 
               4th ed., Oxford Univ. Press, 1971, page 104.
%D A007408 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.
%H A007408 T. D. Noe, <a href="b007408.txt">Table of n, a(n) for n=1..200</a>
%H A007408 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha103.htm">Factorizations of many number sequences</a>
%H A007408 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha1294.htm">Factorizations of many number sequences</a>
%F A007408 Sum[1/k^3, {k, 1, n}] = Sqrt[Sum[Sum[1/(i*j)^3, {i, 1, n}], {j, 1, n}]] 
               - Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 26 2004
%p A007408 A007408:=n->numer(sum(1/k^3,k=1..n)); map(%,[$1..20]); - M. F. Hasler 
               (Maximilian.Hasler(AT)gmail.com), Nov 10 2006
%t A007408 s=0;lst={};Do[s+=n^1/n^4;AppendTo[lst,Numerator[s]],{n,3*4!}];lst [From 
               Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 24 2009]
%Y A007408 Cf. A001008, A007406, A007409.
%Y A007408 Cf. A124787.
%Y A007408 Sequence in context: A012202 A012098 A012072 this_sequence A066989 A160501 
               A075987
%Y A007408 Adjacent sequences: A007405 A007406 A007407 this_sequence A007409 A007410 
               A007411
%K A007408 nonn,frac
%O A007408 1,2
%A A007408 N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein