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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 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.)