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A104407
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Number of hamiltonian groups of order <= n.
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2
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0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,16
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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.
T. Pisanski and T.W. Tucker, The genus of low rank hamiltonian groups, Discrete Math. 78 (1989), 157-167.
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LINKS
| B. Horvat, G. Jaklic and T. Pisanski, On the number of Hamiltonian groups
Eric Weisstein's World of Mathematics, Hamiltonian Group
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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; numberOfHamiltonianGroupsOfOrderLEQThanN[n_]:=Map[Apply[Plus, # ]&, Table[Take[Map[h, Table[i, {i, 1, n}]], i], {i, 1, n}]];
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CROSSREFS
| Cf. A000688, A063966, A104488, A104404, A104452, A104453.
Sequence in context: A133878 A132292 A110656 * A054897 A003108 A111898
Adjacent sequences: A104404 A104405 A104406 * A104408 A104409 A104410
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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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