A225788 a(n) = floor(72*n^(1/2)*(log(n))^(3/2)) for n >= 1, a(0) = 0.

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

Offset: 0

Author

L. Edson Jeffery, May 16 2013

Keywords

• nonn

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.

Programs

Mathematica

Join[{0}, Table[Floor[72*n^(1/2)*(Log[n])^(3/2)], {n, 100}]] (* T. D. Noe, May 23 2013 *)

Extensions

Definition amended by Georg Fischer, Aug 31 2021