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A104407 Number of hamiltonian groups of order <= n. 2
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; text; internal format)
OFFSET

1,16

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..92.

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, 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; numberOfHamiltonianGroupsOfOrderLEQThanN[n_]:=Map[Apply[Plus, # ]&, Table[Take[Map[h, Table[i, {i, 1, n}]], i], {i, 1, n}]];

CROSSREFS

Cf. A000688, A063966, A104488, A104404, A104452, A104453.

Sequence in context: A133878 A132292 A110656 * A054897 A261226 A003108

Adjacent sequences:  A104404 A104405 A104406 * A104408 A104409 A104410

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 January 27 12:01 EST 2020. Contains 331295 sequences. (Running on oeis4.)