A129647 Largest order of a permutation of n elements with exactly 2 cycles. Also the largest LCM of a 2-partition of n.

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

Links

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

Index entries for sequences related to lcm's

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1,-2,1).

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

Cf. A000793, A129651.

Cf. A116921, A116922.

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

Adjacent sequences: A129644 A129645 A129646 * A129648 A129649 A129650

Keyword

nonn,easy

Author

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

Status

approved