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

%I A213206 #17 Feb 18 2013 07:09:16
%S A213206 1,1,1,3,4,5,6,12,15,20,21,30,60,60,84,105,140,140,210,420,420,420,
%T A213206 420,840,840,1260,1260,1540,1540,2520,4620,4620,5460,5460,9240,9240,
%U A213206 13860,13860,16380,16380,27720,27720,32760,60060,60060,60060,60060,120120,120120,180180,180180,180180
%N A213206 Largest order of permutation without a 2-cycle of n elements. Equivalently, largest LCM of partitions of n without parts =2.
%H A213206 Joerg Arndt, <a href="/A213206/b213206.txt">Table of n, a(n) for n = 0..101</a>
%F A213206 a(n) = A000793(n) unless n is a term of A007504 (sum of first primes).
%e A213206 The 11 partitions (including those with parts =2) of 6 are the following:
%e A213206 [ #]  [ partition ]   LCM( parts )
%e A213206 [ 1]  [ 1 1 1 1 1 1 ]   1
%e A213206 [ 2]  [ 1 1 1 1 2 ]   2
%e A213206 [ 3]  [ 1 1 1 3 ]   3
%e A213206 [ 4]  [ 1 1 2 2 ]   2
%e A213206 [ 5]  [ 1 1 4 ]   4
%e A213206 [ 6]  [ 1 2 3 ]   6  (max, with a part =2)
%e A213206 [ 7]  [ 1 5 ]   5
%e A213206 [ 8]  [ 2 2 2 ]   2
%e A213206 [ 9]  [ 2 4 ]   4
%e A213206 [10]  [ 3 3 ]   3
%e A213206 [11]  [ 6 ]   6  (max, without a part =2)
%e A213206 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.
%e A213206 The 7 partitions (including those with parts =2) of 5 are the following:
%e A213206 [ #]  [ partition ]   LCM( parts )
%e A213206 [ 1]  [ 1 1 1 1 1 ]   1
%e A213206 [ 2]  [ 1 1 1 2 ]   2
%e A213206 [ 3]  [ 1 1 3 ]   3
%e A213206 [ 4]  [ 1 2 2 ]   2
%e A213206 [ 5]  [ 1 4 ]   4
%e A213206 [ 6]  [ 2 3 ]   6 (max with a part =2)
%e A213206 [ 7]  [ 5 ]   5  (max, without a part =2)
%e A213206 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.
%K A213206 nonn
%O A213206 0,4
%A A213206 _Joerg Arndt_, Feb 15 2013