cp's OEIS Frontend

A256445 Irregular triangle T(n,k) read by rows: row n gives a largest partition of n with maximal order (see Comments for precise definition).

%I A256445 #30 Apr 01 2015 15:44:46
%S A256445 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 A256445 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 A256445 7,3,5,7,8,1,3,5,7,8,4,5,7,9,1,4,5,7,9
%N A256445 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 A256445 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 A256445 Triangle starts T(1,1) = 1:
%e A256445 1:  1
%e A256445 2:  2
%e A256445 3:  3
%e A256445 4:  4
%e A256445 5:  2,3
%e A256445 6:  1,2,3
%e A256445 7:  3,4
%e A256445 8;  3,5
%e A256445 9:  4,5
%e A256445 10: 2,3,5
%e A256445 11: 1,2,3,5
%e A256445 12: 3,4,5
%e A256445 13: 1,3,4,5
%e A256445 14: 3,4,7
%e A256445 15: 3,5,7
%e A256445 16: 4,5,7
%e A256445 17: 2,3,5,7
%e A256445 18: 1,2,3,5,7
%e A256445 19: 3,4,5,7
%e A256445 20: 1,3,4,5,7
%e A256445 21: 1,1,3,4,5,7
%e A256445 22: 1,1,1,3,4,5,7
%e A256445 23: 3,5,7,8
%e A256445 T(11,k) = [1,2,3,5] rather than [5,6] because [1,2,3,5] has more elements.
%Y A256445 Cf. A000793, A074064, A256443.
%K A256445 nonn,tabf
%O A256445 1,2
%A A256445 _Bob Selcoe_, Mar 29 2015
%E A256445 More terms from _Alois P. Heinz_, Apr 01 2015