A129649 Largest order of a permutation of n elements with exactly 4 cycles. Also the largest LCM of a 4-partition of n.

0, 0, 0, 1, 2, 3, 6, 6, 12, 15, 30, 30, 60, 60, 84, 105, 210, 140, 420, 210, 330, 420, 840, 420, 1260, 1155, 1540, 1365, 2520, 1320, 3080, 3465, 3960, 4095, 5544, 5005, 6930, 6435, 8190, 9009, 10296, 8415, 12870, 11781, 13464, 15015, 18018, 17017, 20592, 21879

Offset: 1

Author

Nickolas Reynolds (nickels(AT)gmail.com), Apr 25 2007

Keywords

• nonn

Comments

a(n) is asymptotic to (n^4)/256.

Examples

			a(18)=140 because 18 = 7+5+2+2 and lcm(2,2,5,7) = 140 is maximal.
		

Links

• Philip Turecek, Table of n, a(n) for n = 1..1000
• Index entries for sequences related to lcm's

Crossrefs

Cf. A000793, A129651.

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).

Programs

Mathematica

Max[LCM @@@ Compositions[ #, 4]] & /@ Range[1, n] (* needs Combinatorica *)
Join[{0,0,0},Table[Max[LCM@@#&/@IntegerPartitions[n,{4}]],{n,4,50}]] (* Harvey P. Dale, Feb 25 2012 *)