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A226143 The smallest k>0 such that A000793(n)^k >= n!. 2

%I

%S 1,1,2,3,3,4,4,4,5,5,6,5,6,6,6,7,7,7,7,8,8,9,8,9,9,9,9,9,10,9,10,10,

%T 10,10,11,11,11,11,11,11,12,12,12,12,12,13,12,13,12,13,13,13,13,13,14,

%U 14,14,14,14,14,14,15,15,15,15,15,15,15,16,15,16,16

%N The smallest k>0 such that A000793(n)^k >= n!.

%C This is a lower bound for A226142(n), the least positive integer k such that S_n is a product of k cyclic groups. Clearly also a(n) = ceiling(log[m](n!) where m = A000793(n).

%H Alois P. Heinz, <a href="/A226143/b226143.txt">Table of n, a(n) for n = 1..10000</a>

%p A000793:=

%p [1,2,3,4,6,6,12,15,20,30,30,60,60,84,105,140,

%p 210,210,420,420,420,420,840,840,1260,1260,1540,

%p 2310,2520,4620,4620,5460,5460,9240,9240,13860,

%p 13860,16380,16380,27720,30030,32760,60060,60060,

%p 60060,60060,120120]:

%p a:=proc(n)

%p global A000793;

%p local k;

%p for k from 1 do

%p if A000793[n]^k >= n! then return k; fi;

%p od;

%p end;

%K nonn

%O 1,3

%A _W. Edwin Clark_, May 27 2013

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Last modified November 18 19:59 EST 2019. Contains 329288 sequences. (Running on oeis4.)