

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
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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



