%I A104488
%S A104488 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,
%T A104488 0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
%U A104488 0,2,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0
%N A104488 Number of Hamiltonian groups of order n.
%D A104488 R. D. Carmichael, Introduction to the Theory of Groups of Finite Order, 
               New York, Dover, 1956.
%D A104488 J. C. Lennox and S. E. Stonehewer, Subnormal Subgroups of Groups, Oxford 
               University Press, 1987.
%D A104488 T. Pisanski and T.W. Tucker, The genus of low rank hamiltonian groups, 
               Discrete Math. 78 (1989), 157-167.
%H A104488 T. D. Noe, <a href="b104488.txt">Table of n, a(n) for n=1..10000</a>
%H A104488 B. Horvat, G. Jaklic and T. Pisanski, <a href="http://arXiv.org/abs/math.CO/
               0503183">On the number of Hamiltonian groups</a>
%H A104488 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HamiltonianGroup.html">Hamiltonian Group</a>
%F A104488 Let n=2^e*o, where e=e(n)>=0 and o=o(n) is an odd number. The number 
               h(n) of hamiltonian groups of order n is given by h(n)=0, if e(n)<3 
               and h(n)=a(o(n)), otherwise, where a(n) denotes the number of Abelian 
               groups of order n.
%t A104488 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;
%Y A104488 Cf. A000688, A104404, A104404, A104452, A104453.
%Y A104488 Sequence in context: A114099 A028613 A024362 this_sequence A010103 A086078 
               A014082
%Y A104488 Adjacent sequences: A104485 A104486 A104487 this_sequence A104489 A104490 
               A104491
%K A104488 nonn,easy,nice
%O A104488 1,72
%A A104488 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