A129648 Largest order of a permutation of n elements with exactly 3 cycles. Also the largest LCM of a 3-partition of n.

0, 0, 1, 2, 3, 6, 6, 12, 15, 30, 21, 60, 35, 84, 105, 140, 84, 210, 165, 280, 315, 360, 385, 504, 495, 630, 693, 792, 819, 990, 1001, 1170, 1287, 1430, 1365, 1716, 1683, 2002, 2145, 2310, 2431, 2730, 2805, 3120, 3315, 3570, 3705, 4080, 4199, 4560, 4845, 5168

Offset: 1

Author

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

Keywords

• nonn

Comments

a(n) is asymptotic to (n^3)/27.

Examples

			a(9) = 15 because 9 = 5+3+1 and lcm(1,3,5) = 15 is maximal.
		

Links

• Alois P. Heinz, 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), this sequence (k=3), A129649 (k=4), A129650 (k=5), A355367 (k=6), A355403 (k=7).

Programs

Mathematica

Max[LCM @@@ Compositions[ #, 3]] & /@ Range[1, n]