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URL: https://oeis.org/A129647

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A129647
Largest order of a permutation of n elements with exactly 2 cycles. Also the largest LCM of a 2-partition of n.
8
0, 1, 2, 3, 6, 5, 12, 15, 20, 21, 30, 35, 42, 45, 56, 63, 72, 77, 90, 99, 110, 117, 132, 143, 156, 165, 182, 195, 210, 221, 240, 255, 272, 285, 306, 323, 342, 357, 380, 399, 420, 437, 462, 483, 506, 525, 552, 575, 600, 621, 650, 675, 702, 725, 756, 783, 812, 837
OFFSET
1,3
COMMENTS
a(n) is asymptotic to (n^2)/4.
a(n) = A116921(n)*A116922(n). - Mamuka Jibladze, Aug 22 2019
FORMULA
G.f.: t^2*(1 + 2*t^3 - 5*t^4 + 8*t^5 - 4*t^6)/((1-t)^2*(1-t^4)). - Mamuka Jibladze, Aug 22 2019
EXAMPLE
a(26) = 165 because 26 = 11+15 and lcm(11,15) = 165 is maximal.
MAPLE
a:= n-> `if`(n<2, 0, max(seq(ilcm(i, n-i), i=1..n/2))):
seq(a(n), n=1..60); # Alois P. Heinz, Feb 16 2013
MATHEMATICA
Join[{0}, Rest[With[{n = 60}, Max[LCM @@@ IntegerPartitions[#, {2}]] & /@ Range[1, n]]]] (* Modified by Philip Turecek, Mar 25 2023 *)
a[n_] := If[n<2, 0, Max[Table[LCM[i, n-i], {i, 1, n/2}]]]; Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Jul 15 2015, after Alois P. Heinz *)
CROSSREFS
Maximal LCM of k positive integers with sum n for k = 2..7: this sequence (k=2), A129648 (k=3), A129649 (k=4), A129650 (k=5), A355367 (k=6), A355403 (k=7).
Sequence in context: A002517 A253568 A053570 * A225652 A136183 A100211
KEYWORD
nonn,easy
AUTHOR
Nickolas Reynolds (nickels(AT)gmail.com), Apr 25 2007
STATUS
approved