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 A104452 Number of groups of order <= n all of whose subgroups are normal. 3
 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, 46, 48, 49, 50, 51, 59, 60, 61, 62, 66, 67, 68, 69, 73, 74, 75, 76, 78, 80, 81, 82, 88, 90, 92, 93, 95, 96, 99, 100, 104, 105, 106, 107, 109, 110, 111, 113, 125, 126, 127 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES R. D. Carmichael, Introduction to the Theory of Groups of Finite Order, New York, Dover, 1956. J. C. Lennox, S. E. Stonehewer, Subnormal Subgroups of Groups, Oxford University Press, 1987. LINKS B. Horvat, G. Jaklic and T. Pisanski, On the number of Hamiltonian groups, arXiv:math/0503183 [math.CO], 2005. T. Pisanski and T.W. Tucker, The genus of low rank hamiltonian groups, Discrete Math. 78 (1989), 157-167. Eric Weisstein's World of Mathematics, Abelian Group Eric Weisstein's World of Mathematics, Hamiltonian Group MATHEMATICA 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]; CROSSREFS Cf. A000688, A063966, A104488, A104407, A104404, A104453. Sequence in context: A285528 A151894 A028229 * A335073 A344514 A062877 Adjacent sequences:  A104449 A104450 A104451 * A104453 A104454 A104455 KEYWORD nonn,easy AUTHOR Boris Horvat (Boris.Horvat(AT)fmf.uni-lj.si), Gasper Jaklic (Gasper.Jaklic(AT)fmf.uni-lj.si), Tomaz Pisanski, Apr 19 2005 STATUS approved

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Last modified June 20 10:07 EDT 2021. Contains 345162 sequences. (Running on oeis4.)