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 A104453 Smallest order for which there are n nonisomorphic finite Hamiltonian groups, or 0 if no such order exists. 3
 8, 72, 216, 1800, 648, 5400, 1944, 88200, 27000, 16200, 10, 5832, 264600, 0, 48600, 17496, 10672200, 0, 1323000, 0, 793800, 20, 243000, 52488, 0, 32016600, 405000, 0, 9261000, 2381400, 0, 157464 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES 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. LINKS 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 FORMULA S_h(n) denotes the smallest number k for which exactly n nonisomorphic hamiltonian groups of order k exist. Here 0 indicates the case when n is not a product of partition numbers and S_h(n) does not exist. CROSSREFS Cf. A000688, A063966, A104488, A104407, A104404, A104452. Sequence in context: A043932 A064015 A044576 * A254371 A143945 A239095 Adjacent sequences: A104450 A104451 A104452 * A104454 A104455 A104456 KEYWORD nonn,hard 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 February 7 22:58 EST 2023. Contains 360132 sequences. (Running on oeis4.)