login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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, 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 (list; graph; refs; listen; history; text; internal format)
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 * A070981 A107228 A294247

Adjacent sequences:  A213203 A213204 A213205 * A213207 A213208 A213209

KEYWORD

nonn

AUTHOR

Joerg Arndt, Feb 15 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 18 17:56 EST 2017. Contains 294894 sequences.