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 A104407 Number of Hamiltonian groups of order <= n. 3
 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 Robert D. Carmichael, Introduction to the Theory of Groups of Finite Order, New York, Dover, 1956. John C. Lennox and Stewart. E. Stonehewer, Subnormal Subgroups of Groups, Oxford University Press, 1987. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 Boris Horvat, Gašper Jaklič, and Tomaž Pisanski, On the number of hamiltonian groups, Mathematical Communications, Vol. 10, No. 1 (2005), pp. 89-94; arXiv preprint, arXiv:math/0503183 [math.CO], 2005. Tomaž Pisanski and Thomas W. Tucker, The genus of low rank hamiltonian groups, Discrete Math. 78 (1989), 157-167. Eric Weisstein's World of Mathematics, Hamiltonian Group. FORMULA a(n) ~ c * n, where c = A021002 * A048651 / 4 = 0.16568181590156732257... . - Amiram Eldar, Oct 03 2023 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 Partial sums of A104488. Cf. A000688, A021002, A048651, A063966, 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 May 26 01:40 EDT 2024. Contains 372807 sequences. (Running on oeis4.)