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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

Table of n, a(n) for n=1..66.

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.)