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 A212721 Triangle read by rows: n-th row gives distinct products of partitions of n (A000041). 6
 1, 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 16, 18, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 24, 27, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS A034891(n) = length of n-th row; A000792(n) = largest term of n-th row; for n>5: A007918(n) = smallest number <= A000792(n) not occurring in n-th row. LINKS Reinhard Zumkeller, Rows n = 0..36 of triangle, flattened EXAMPLE A000041(6)=11, the 11 partitions and their products of 6:    1: (1,1,1,1,1,1)   ->   1 * 1 * 1 * 1 * 1 * 1 = 1    2: (1,1,1,1,2)     ->   1 * 1 * 1 * 1 * 2     = 2    3: (1,1,1,3)       ->   1 * 1 * 1 * 3         = 3    4: (1,1,2,2)       ->   1 * 1 * 2 * 2         = 4    5: (1,1,4)         ->   1 * 1 * 4             = 4    6: (1,2,3)         ->   1 * 2 * 3             = 6    7: (1,5)           ->   1 * 5                 = 5    8: (2,2,2)         ->   2 * 2 * 2             = 8    9: (2,4)           ->   2 * 4                 = 8   10: (3,3)           ->   3 * 3                 = 9   11: (6)             ->                           6, sorted and duplicates removed: T(6,1..8)=[1,2,3,4,5,6,8,9], A034891(6)=8. The triangle begins:    0 |  [1]    1 |  [1]    2 |  [1,2]    3 |  [1,2,3]    4 |  [1,2,3,4]    5 |  [1,2,3,4,5,6]    6 |  [1,2,3,4,5,6,8,9]    7 |  [1,2,3,4,5,6,7,8,9,10,12]    8 |  [1,2,3,4,5,6,7,8,9,10,12,15,16,18]    9 |  [1,2,3,4,5,6,7,8,9,10,12,14,15,16,18,20,24,27]   10 |  [1,2,3,4,5,6,7,8,9,10,12,14,15,16,18,20,21,24,25,27,30,32,36]. MATHEMATICA row[n_] := Union[Times @@@ IntegerPartitions[n]]; Table[row[n], {n, 0, 10}] (* Jean-François Alcover, Jun 29 2019 *) PROG (Haskell) import Data.List (nub, sort) a212721 n k = a212721_row n !! (k-1) a212721_row = nub . sort . (map product) . ps 1 where    ps x 0 = [[]]    ps x y = [t:ts | t <- [x..y], ts <- ps t (y - t)] a212721_tabf = map a212721_row [0..] (Sage) [sorted(list(set([mul(p) for p in Partitions(n)]))) for n in range(11)] # Peter Luschny, Dec 13 2015 CROSSREFS Cf. A000041, A000792, A034891. Sequence in context: A243712 A256553 A194896 * A222417 A253573 A229945 Adjacent sequences:  A212718 A212719 A212720 * A212722 A212723 A212724 KEYWORD nonn,tabf,look AUTHOR Reinhard Zumkeller, Jun 14 2012 STATUS approved

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Last modified May 18 23:31 EDT 2022. Contains 353826 sequences. (Running on oeis4.)