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A104404
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Number of groups of order n all of whose subgroups are normal.
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4
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1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 2, 1, 1, 1, 6, 1, 2, 1, 2, 1, 1, 1, 4, 2, 1, 3, 2, 1, 1, 1, 8, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 2, 2, 1, 1, 6, 2, 2, 1, 2, 1, 3, 1, 4, 1, 1, 1, 2, 1, 1, 2, 12, 1, 1, 1, 2, 1, 1, 1, 8, 1, 1, 2, 2, 1, 1, 1, 6, 5, 1, 1, 2, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 8, 1, 2, 2, 4, 1, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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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.
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LINKS
| B. Horvat, G. Jaklic and T. Pisanski, On the number of Hamiltonian groups
Eric Weisstein's World of Mathematics, Abelian Group
Eric Weisstein's World of Mathematics, Hamiltonian Group
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FORMULA
| The number b(n) of all groups of order n all of whose subgroups are normal is given as b(n)=a(n)+h(n), where a(n) denotes the number of Abelian groups of order n and h(n) denotes the number of Hamiltonian groups of order n.
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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; b[n_]:= a[n]+h[n];
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CROSSREFS
| Cf. A000688, A000001.
Sequence in context: A133910 A066441 A173398 * A162512 A162510 A181876
Adjacent sequences: A104401 A104402 A104403 * A104405 A104406 A104407
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KEYWORD
| nonn,easy
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AUTHOR
| 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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