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%I #21 Aug 31 2021 11:32:40
%S 0,0,58,143,235,328,422,517,610,703,795,886,976,1066,1154,1242,1329,
%T 1415,1501,1585,1669,1752,1835,1917,1998,2079,2159,2238,2317,2395,
%U 2473,2551,2627,2704,2780,2855,2930,3005,3079,3152,3226,3299,3371,3443,3515,3587
%N a(n) = floor(72*n^(1/2)*(log(n))^(3/2)) for n >= 1, a(0) = 0.
%C 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.
%H Miklós Abért, <a href="http://dx.doi.org/10.1112/S0024609302001042">Symmetric groups as products of Abelian subgroups</a>, Bull. Lond. Math. Soc., Volume 34, Issue 04, July 2002, pp. 451-456.
%H R. Bercov and L. Moser, <a href="http://dx.doi.org/10.4153/CMB-1965-045-6">On Abelian permutation groups</a>, Canad. Math. Bull. 8 (1965) 627-630.
%t Join[{0}, Table[Floor[72*n^(1/2)*(Log[n])^(3/2)], {n, 100}]] (* _T. D. Noe_, May 23 2013 *)
%K nonn
%O 0,3
%A _L. Edson Jeffery_, May 16 2013
%E Definition amended by _Georg Fischer_, Aug 31 2021
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