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

1,2

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). 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.

Links

Table of n, a(n) for n=1..87.

Example

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.

Crossrefs

Cf. A000793, A074064, A256443.

Sequence in context: A264809 A035578 A227784 * A275103 A359729 A107795

Adjacent sequences: A256442 A256443 A256444 * A256446 A256447 A256448

Keyword

nonn,tabf

Author

Bob Selcoe, Mar 29 2015

Extensions

More terms from Alois P. Heinz, Apr 01 2015

Status

approved