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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. 6
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 (list; graph; refs; listen; history; text; internal format)
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 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

Max[LCM @@@ Compositions[ #, 2]]& /@ Range[1, n]

a[n_] := If[n<2, 0, Max[Table[LCM[i, n-i], {i, 1, n/2}]]]; Table[a[n], {n, 1, 60}] (* Jean-Fran├žois Alcover, Jul 15 2015, after Alois P. Heinz *)

CROSSREFS

Cf. A000793, A129648, A129649, A129650, A129651.

Cf. A116921, A116922.

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

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Last modified November 19 16:37 EST 2019. Contains 329323 sequences. (Running on oeis4.)