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 A226143 The smallest k>0 such that A000793(n)^k >= n!. 2
 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, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 12, 13, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 16, 15, 16, 16 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 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). LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 MAPLE A000793:= [1, 2, 3, 4, 6, 6, 12, 15, 20, 30, 30, 60, 60, 84, 105, 140, 210, 210, 420, 420, 420, 420, 840, 840, 1260, 1260, 1540, 2310, 2520, 4620, 4620, 5460, 5460, 9240, 9240, 13860, 13860, 16380, 16380, 27720, 30030, 32760, 60060, 60060, 60060, 60060, 120120]: a:=proc(n) global A000793; local k; for k from 1 do if A000793[n]^k >= n! then return k; fi; od; end; CROSSREFS Sequence in context: A189641 A189672 A058889 * A166724 A110862 A104257 Adjacent sequences:  A226140 A226141 A226142 * A226144 A226145 A226146 KEYWORD nonn AUTHOR W. Edwin Clark, May 27 2013 STATUS approved

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Last modified October 21 06:39 EDT 2019. Contains 328292 sequences. (Running on oeis4.)