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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 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.)