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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
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 (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). 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 A107795 A274917

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

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Last modified March 23 14:17 EDT 2019. Contains 321431 sequences. (Running on oeis4.)