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A256443 Irregular triangle T(n,k) read by rows: row n gives a smallest partition of n with maximal order (see Comments for precise definition).

%I A256443 #24 Apr 01 2015 15:44:19
%S A256443 1,2,3,4,2,3,6,3,4,3,5,4,5,2,3,5,5,6,3,4,5,1,3,4,5,3,4,7,3,5,7,4,5,7,
%T A256443 2,3,5,7,5,6,7,3,4,5,7,1,3,4,5,7,2,3,4,5,7,4,5,6,7,3,5,7,8,1,3,5,7,8,
%U A256443 4,5,7,9,1,4,5,7,9,4,5,7,11,2,3,5,7,11
%N A256443 Irregular triangle T(n,k) read by rows: row n gives a smallest partition of n with maximal order (see Comments for precise definition).
%C A256443 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). Minimize the number of parts. Then take the lexicographically earliest solution. This is row n of the triangle. See  A256445 for a partition with the most elements.
%e A256443 Triangle starts T(1,1) = 1:
%e A256443 1:  1
%e A256443 2:  2
%e A256443 3:  3
%e A256443 4:  4
%e A256443 5:  2,3
%e A256443 6:  6
%e A256443 7:  3,4
%e A256443 8:  3,5
%e A256443 9:  4,5
%e A256443 10: 2,3,5
%e A256443 11: 5,6
%e A256443 12: 3,4,5
%e A256443 13: 1,3,4,5
%e A256443 14: 3,4,7
%e A256443 15: 3,5,7
%e A256443 16: 4,5,7
%e A256443 17: 2,3,5,7
%e A256443 18: 5,6,7
%e A256443 19: 3,4,5,7
%e A256443 20: 1,3,4,5,7
%e A256443 21: 2,3,4,5,7
%e A256443 22: 4,5,6,7
%e A256443 23: 3,5,7,8
%e A256443 T(11,k) = [5,6] rather than [1,2,3,5] because [5,6] has fewer elements.
%Y A256443 Cf. A000793, A074064, A256445.
%K A256443 nonn,tabf
%O A256443 1,2
%A A256443 _Bob Selcoe_, Mar 29 2015
%E A256443 More terms from _Alois P. Heinz_, Apr 01 2015