Search: id:A104452
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%I A104452
%S A104452 1,2,3,5,6,7,8,12,14,15,16,18,19,20,21,27,28,30,31,33,34,35,36,40,42,43,
%T A104452 46,48,49,50,51,59,60,61,62,66,67,68,69,73,74,75,76,78,80,81,82,88,90,
%U A104452 92,93,95,96,99,100,104,105,106,107,109,110,111,113,125,126,127
%N A104452 Number of groups of order <= n all of whose subgroups are normal.
%D A104452 R. D. Carmichael, Introduction to the Theory of Groups of Finite Order, 
               New York, Dover, 1956.
%D A104452 J. C. Lennox, S.E. Stonehewer, Subnormal Subgroups of Groups, Oxford 
               University Press, 1987.
%D A104452 T. Pisanski, T.W. Tucker, The genus of low rank hamiltonian groups, Discrete 
               Math. 78 (1989), 157-167.
%H A104452 B. Horvat, G. Jaklic and T. Pisanski, <a href="http://arXiv.org/abs/math.CO/
               0503183">On the number of Hamiltonian groups</a>
%H A104452 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               AbelianGroup.html">Abelian Group</a>
%H A104452 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HamiltonianGroup.html">Hamiltonian Group</a>
%t A104452 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; numberOfAbelianGroupsOfOrderLEQThanN[n_]:=Map[Apply[Plus, 
               # ]&, Table[Take[Map[a, Table[i, {i, 1, n}]], i], {i, 1, n}]]; numberOfHamiltonianGroupsOfOrderLEQThanN[n\
               _]:=Map[Apply[Plus, # ]&, Table[Take[Map[h, Table[i, {i, 1, n}]], 
               i], {i, 1, n}]]; numberOfAllGroupsOfOrderLEQThanN[n_]:=numberOfAbelianGroupsOfOrderLEQThanN[n] 
               +numberOfHamiltonianGroupsOfOrderLEQThanN[n];
%Y A104452 Cf. A000688, A063966, A104488, A104407, A104404, A104453.
%Y A104452 Sequence in context: A006431 A151894 A028229 this_sequence A062877 A068526 
               A039086
%Y A104452 Adjacent sequences: A104449 A104450 A104451 this_sequence A104453 A104454 
               A104455
%K A104452 nonn,easy
%O A104452 1,2
%A A104452 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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