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).

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, 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, 4, 5, 7, 9, 1, 4, 5, 7, 9, 4, 5, 7, 11, 2, 3, 5, 7, 11

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..86.

Example

Triangle starts T(1,1) = 1:
1:  1
2:  2
3:  3
4:  4
5:  2,3
6:  6
7:  3,4
8:  3,5
9:  4,5
10: 2,3,5
11: 5,6
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: 5,6,7
19: 3,4,5,7
20: 1,3,4,5,7
21: 2,3,4,5,7
22: 4,5,6,7
23: 3,5,7,8
T(11,k) = [5,6] rather than [1,2,3,5] because [5,6] has fewer elements.

Crossrefs

Cf. A000793, A074064, A256445.

Sequence in context: A304112 A293446 A360378 * A046068 A166281 A330954

Adjacent sequences: A256440 A256441 A256442 * A256444 A256445 A256446

Keyword

nonn,tabf

Author

Bob Selcoe, Mar 29 2015

Extensions

More terms from Alois P. Heinz, Apr 01 2015

Status

approved