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Search: id:A104488
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| A104488 |
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Number of Hamiltonian groups of order n. |
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+0
4
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| 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0
(list; graph; listen)
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OFFSET
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1,72
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REFERENCES
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R. D. Carmichael, Introduction to the Theory of Groups of Finite Order, New York, Dover, 1956.
J. C. Lennox and 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
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T. D. Noe, Table of n, a(n) for n=1..10000
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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FORMULA
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Let n=2^e*o, where e=e(n)>=0 and o=o(n) is an odd number. The number h(n) of hamiltonian groups of order n is given by h(n)=0, if e(n)<3 and h(n)=a(o(n)), otherwise, where a(n) denotes the number of Abelian groups of order n.
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MATHEMATICA
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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;
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CROSSREFS
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Cf. A000688, A104404, A104404, A104452, A104453.
Sequence in context: A114099 A028613 A024362 this_sequence A010103 A086078 A014082
Adjacent sequences: A104485 A104486 A104487 this_sequence A104489 A104490 A104491
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KEYWORD
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nonn,easy,nice
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AUTHOR
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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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