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A129649
Largest order of a permutation of n elements with exactly 4 cycles. Also the largest LCM of a 4-partition of n.
8
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.
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
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
KEYWORD
nonn
AUTHOR
Nickolas Reynolds (nickels(AT)gmail.com), Apr 25 2007
STATUS
approved