

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
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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). 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



