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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). 1
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 (list; graph; refs; listen; history; text; internal format)
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: A304113 A304112 A293446 * 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

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Last modified April 19 07:36 EDT 2021. Contains 343109 sequences. (Running on oeis4.)