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

1,4

Comments

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

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Index entries for sequences related to lcm's

Example

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

Mathematica

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

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).

Sequence in context: A131259 A346758 A143177 * A129649 A129650 A355367

Adjacent sequences: A129645 A129646 A129647 * A129649 A129650 A129651

Keyword

nonn

Author

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

Status

approved