Search: id:A104407
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%I A104407
%S A104407 0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,
%T A104407 4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,
%U A104407 8,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,12,12,12,12,12
%N A104407 Number of hamiltonian groups of order <= n.
%D A104407 R. D. Carmichael, Introduction to the Theory of Groups of Finite Order, 
               New York, Dover, 1956.
%D A104407 J. C. Lennox, S.E. Stonehewer, Subnormal Subgroups of Groups, Oxford 
               University Press, 1987.
%D A104407 T. Pisanski and T.W. Tucker, The genus of low rank hamiltonian groups, 
               Discrete Math. 78 (1989), 157-167.
%H A104407 B. Horvat, G. Jaklic and T. Pisanski, <a href="http://arXiv.org/abs/math.CO/
               0503183">On the number of Hamiltonian groups</a>
%H A104407 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HamiltonianGroup.html">Hamiltonian Group</a>
%t A104407 orders[n_]:=Map[Last, FactorInteger[n]]; a[n_]:=Apply[Times, Map[PartitionsP, 
               orders[n]]]; e[n_]:=n/ 2^IntegerExponent[n, 2]; h[n_]/;Mod[n, 8]==0:=a[e[n]]; 
               h[n_]:=0; numberOfHamiltonianGroupsOfOrderLEQThanN[n_]:=Map[Apply[Plus, 
               # ]&, Table[Take[Map[h, Table[i, {i, 1, n}]], i], {i, 1, n}]];
%Y A104407 Cf. A000688, A063966, A104488, A104404, A104452, A104453.
%Y A104407 Sequence in context: A133878 A132292 A110656 this_sequence A054897 A003108 
               A111898
%Y A104407 Adjacent sequences: A104404 A104405 A104406 this_sequence A104408 A104409 
               A104410
%K A104407 nonn,easy
%O A104407 1,16
%A A104407 Boris Horvat (Boris.Horvat(AT)fmf.uni-lj.si), Gasper Jaklic (Gasper.Jaklic(AT)fmf.uni-lj.si), 
               Tomaz Pisanski (Tomaz.Pisanski(AT)fmf.uni-lj.si), Apr 19 2005

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