

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
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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 (* JeanFrançois Alcover, Feb 02 2015 *)


PROG

(Haskell)
a070861 n = a070861_list !! (n1)
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^(n1), i, factorback(vecextract(v, i1)))) \\ 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



