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A070861 Triangle of all possible distinct numbers obtained as a product of distinct numbers from 1..n. 5
1, 1, 2, 1, 2, 3, 6, 1, 2, 3, 4, 6, 8, 12, 24, 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 20, 24, 30, 36, 40, 48, 60, 72, 90, 120, 144, 180, 240, 360, 720, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Factorials are a subsequence (A000142). - Reinhard Zumkeller, Jul 02 2011

More generally, all sequences of positive integers are subsequences. - Charles R Greathouse IV, Mar 06 2017

LINKS

Reinhard Zumkeller, Rows n=1..20 of triangle, flattened

EXAMPLE

Triangle begins

1;

1,2;

1,2,3,6;

1,2,3,4,6,8,12,24; ...

MATHEMATICA

row[n_] := Times @@@ Subsets[Range[n]] // Flatten // Union; Table[row[n], {n, 1, 20}] // Flatten (* Jean-François Alcover, Feb 02 2015 *)

PROG

(Haskell)

a070861 n = a070861_list !! (n-1)

a070861_list = concat a070861_tabf

a070861_tabf = [1] : f 2 [1] where

   f n ps = ps' : f (n+1) ps' where ps' = m ps $ map (n*) ps

   m []         ys = ys

   m xs'@(x:xs) ys'@(y:ys)

       | x < y     = x : m xs ys'

       | x == y    = x : m xs ys

       | otherwise = y : m xs' ys

b070861 = bFile' "A070861" (concat $ take 20 a070861_tabf) 1

-- Reinhard Zumkeller, Jul 02 2011

(PARI) row(n)=my(v=[2..n]); Set(vector(2^(n-1), i, factorback(vecextract(v, i-1)))) \\ Charles R Greathouse IV, Mar 06 2017

CROSSREFS

Cf. A060957, A070863.

Sequence in context: A078777 A135938 A079210 * A277566 A261144 A106524

Adjacent sequences:  A070858 A070859 A070860 * A070862 A070863 A070864

KEYWORD

nonn,tabf

AUTHOR

Amarnath Murthy, May 16 2002

EXTENSIONS

Corrected and extended by Lior Manor May 23 2002

STATUS

approved

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Last modified December 2 17:59 EST 2021. Contains 349445 sequences. (Running on oeis4.)