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%I #22 Mar 28 2023 07:58:48
%S 0,0,0,1,2,3,6,6,12,15,30,30,60,60,84,105,210,140,420,210,330,420,840,
%T 420,1260,1155,1540,1365,2520,1320,3080,3465,3960,4095,5544,5005,6930,
%U 6435,8190,9009,10296,8415,12870,11781,13464,15015,18018,17017,20592,21879
%N Largest order of a permutation of n elements with exactly 4 cycles. Also the largest LCM of a 4-partition of n.
%C a(n) is asymptotic to (n^4)/256.
%H Philip Turecek, <a href="/A129649/b129649.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>
%e a(18)=140 because 18 = 7+5+2+2 and lcm(2,2,5,7) = 140 is maximal.
%t Max[LCM @@@ Compositions[ #, 4]] & /@ Range[1, n] (* needs Combinatorica *)
%t Join[{0,0,0},Table[Max[LCM@@#&/@IntegerPartitions[n,{4}]],{n,4,50}]] (* _Harvey P. Dale_, Feb 25 2012 *)
%Y Cf. A000793, A129651.
%Y Maximal LCM of k positive integers with sum n for k = 2..7: A129647 (k=2), A129648 (k=3), this sequence (k=4), A129650 (k=5), A355367 (k=6), A355403 (k=7).
%K nonn
%O 1,5
%A Nickolas Reynolds (nickels(AT)gmail.com), Apr 25 2007
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