login
A070861
Triangle of all possible distinct numbers obtained as a product of distinct numbers from 1..n.
5
1, 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
OFFSET
0,4
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
FORMULA
T(n,A060957(n)) = A000142(n) = n!. - Alois P. Heinz, Aug 01 2022
EXAMPLE
Triangle begins:
1;
1;
1, 2;
1, 2, 3, 6;
1, 2, 3, 4, 6, 8, 12, 24;
...
MAPLE
T:= proc(n) option remember; `if`(n=0, 1,
sort([map(x-> [x, x*n][], {T(n-1)})[]])[])
end:
seq(T(n), n=0..7); # Alois P. Heinz, Aug 01 2022
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
Row sums give A070863.
Row products give A283261.
Sequence in context: A078777 A135938 A079210 * A277566 A261144 A106524
KEYWORD
nonn,tabf
AUTHOR
Amarnath Murthy, May 16 2002
EXTENSIONS
Corrected and extended by Lior Manor May 23 2002
Row n=0 prepended by Alois P. Heinz, Aug 01 2022
STATUS
approved