

A213206


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


1



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
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OFFSET

0,4


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).


EXAMPLE

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.


CROSSREFS

Sequence in context: A177431 A145735 A228943 * A299496 A070981 A107228
Adjacent sequences: A213203 A213204 A213205 * A213207 A213208 A213209


KEYWORD

nonn


AUTHOR

Joerg Arndt, Feb 15 2013


STATUS

approved



