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

1,5

Comments

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

Links

Philip Turecek, Table of n, a(n) for n = 1..1000

Index entries for sequences related to lcm's

Example

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

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 *)

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).

Sequence in context: A346758 A143177 A129648 * A129650 A355367 A355403

Adjacent sequences: A129646 A129647 A129648 * A129650 A129651 A129652

Keyword

nonn

Author

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

Status

approved