A256445 - OEIS

%I #30 Apr 01 2015 15:44:46

%S 1,2,3,4,2,3,1,2,3,3,4,3,5,4,5,2,3,5,1,2,3,5,3,4,5,1,3,4,5,3,4,7,3,5,

%T 7,4,5,7,2,3,5,7,1,2,3,5,7,3,4,5,7,1,3,4,5,7,1,1,3,4,5,7,1,1,1,3,4,5,

%U 7,3,5,7,8,1,3,5,7,8,4,5,7,9,1,4,5,7,9

%N Irregular triangle T(n,k) read by rows: row n gives a largest partition of n with maximal order (see Comments for precise definition).

%C Consider all partitions of n for which the LCM of the parts is A000793(n) (A000793 is Landau's function g(n), the largest order of a permutation of n elements). Maximize the number of parts. Then take the lexicographically earliest solution. This is row n of the triangle. See A256443 for a partition with the fewest elements.

%e Triangle starts T(1,1) = 1:

%e 1:  1

%e 2:  2

%e 3:  3

%e 4:  4

%e 5:  2,3

%e 6:  1,2,3

%e 7:  3,4

%e 8;  3,5

%e 9:  4,5

%e 10: 2,3,5

%e 11: 1,2,3,5

%e 12: 3,4,5

%e 13: 1,3,4,5

%e 14: 3,4,7

%e 15: 3,5,7

%e 16: 4,5,7

%e 17: 2,3,5,7

%e 18: 1,2,3,5,7

%e 19: 3,4,5,7

%e 20: 1,3,4,5,7

%e 21: 1,1,3,4,5,7

%e 22: 1,1,1,3,4,5,7

%e 23: 3,5,7,8

%e T(11,k) = [1,2,3,5] rather than [5,6] because [1,2,3,5] has more elements.

%Y Cf. A000793, A074064, A256443.

%K nonn,tabf

%O 1,2

%A _Bob Selcoe_, Mar 29 2015

%E More terms from _Alois P. Heinz_, Apr 01 2015