A213206 Largest order of permutation without a 2-cycle of n elements. Equivalently, largest LCM of partitions of n without parts =2.

1, 1, 1, 3, 4, 5, 6, 12, 15, 20, 21, 30, 60, 60, 84, 105, 140, 140, 210, 420, 420, 420, 420, 840, 840, 1260, 1260, 1540, 1540, 2520, 4620, 4620, 5460, 5460, 9240, 9240, 13860, 13860, 16380, 16380, 27720, 27720, 32760, 60060, 60060, 60060, 60060, 120120, 120120, 180180, 180180, 180180

Offset: 0

Author

Joerg Arndt, Feb 15 2013

Keywords

• nonn

Examples

			The 11 partitions (including those with parts =2) of 6 are the following:
[ #]  [ partition ]   LCM( parts )
[ 1]  [ 1 1 1 1 1 1 ]   1
[ 2]  [ 1 1 1 1 2 ]   2
[ 3]  [ 1 1 1 3 ]   3
[ 4]  [ 1 1 2 2 ]   2
[ 5]  [ 1 1 4 ]   4
[ 6]  [ 1 2 3 ]   6  (max, with a part =2)
[ 7]  [ 1 5 ]   5
[ 8]  [ 2 2 2 ]   2
[ 9]  [ 2 4 ]   4
[10]  [ 3 3 ]   3
[11]  [ 6 ]   6  (max, without a part =2)
The largest order 6 is obtained twice, the first such partition is forbidden for this sequence, but not the second, so a(6) = A000793(6) = 6.
The 7 partitions (including those with parts =2) of 5 are the following:
[ #]  [ partition ]   LCM( parts )
[ 1]  [ 1 1 1 1 1 ]   1
[ 2]  [ 1 1 1 2 ]   2
[ 3]  [ 1 1 3 ]   3
[ 4]  [ 1 2 2 ]   2
[ 5]  [ 1 4 ]   4
[ 6]  [ 2 3 ]   6 (max with a part =2)
[ 7]  [ 5 ]   5  (max, without a part =2)
The largest order (A000793(5)=6) with a part =2 is obtained with the partition into distinct primes; the largest order without a part =2 is a(5)=5.
		

Links

• Joerg Arndt, Table of n, a(n) for n = 0..101

Formula

a(n) = A000793(n) unless n is a term of A007504 (sum of first primes).