A256443 -id:A256443 - 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).

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

Offset: 1

Bob Selcoe, Mar 29 2015

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.

			Triangle starts T(1,1) = 1:
1:  1
2:  2
3:  3
4:  4
5:  2,3
6:  1,2,3
7:  3,4
8;  3,5
9:  4,5
10: 2,3,5
11: 1,2,3,5
12: 3,4,5
13: 1,3,4,5
14: 3,4,7
15: 3,5,7
16: 4,5,7
17: 2,3,5,7
18: 1,2,3,5,7
19: 3,4,5,7
20: 1,3,4,5,7
21: 1,1,3,4,5,7
22: 1,1,1,3,4,5,7
23: 3,5,7,8
T(11,k) = [1,2,3,5] rather than [5,6] because [1,2,3,5] has more elements.

Cf. A000793, A074064, A256443.

More terms from Alois P. Heinz, Apr 01 2015

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).

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