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 A225788 a(n) = floor(72*n^(1/2)*(log(n))^(3/2)) for n >= 1, a(0) = 0. 1
 0, 0, 58, 143, 235, 328, 422, 517, 610, 703, 795, 886, 976, 1066, 1154, 1242, 1329, 1415, 1501, 1585, 1669, 1752, 1835, 1917, 1998, 2079, 2159, 2238, 2317, 2395, 2473, 2551, 2627, 2704, 2780, 2855, 2930, 3005, 3079, 3152, 3226, 3299, 3371, 3443, 3515, 3587 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Miklós Abért proved that the symmetric group S_n is a product of at most 72*n^(1/2)*(log(n))^(3/2) cyclic subgroups. Here we have taken the floor of the upper bound stated in the reference in which the author also states the lower bound of (1 + o(1))*(n*log(n))^(1/2) cyclic subgroups. LINKS Miklós Abért, Symmetric groups as products of Abelian subgroups, Bull. Lond. Math. Soc., Volume 34, Issue 04, July 2002, pp. 451-456. R. Bercov and L. Moser, On Abelian permutation groups, Canad. Math. Bull. 8 (1965) 627-630. MATHEMATICA Join[{0}, Table[Floor[72*n^(1/2)*(Log[n])^(3/2)], {n, 100}]] (* T. D. Noe, May 23 2013 *) CROSSREFS Sequence in context: A044309 A044690 A118153 * A250733 A108750 A044390 Adjacent sequences:  A225785 A225786 A225787 * A225789 A225790 A225791 KEYWORD nonn AUTHOR L. Edson Jeffery, May 16 2013 EXTENSIONS Definition amended by Georg Fischer, Aug 31 2021 STATUS approved

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Last modified July 4 20:49 EDT 2022. Contains 355086 sequences. (Running on oeis4.)