A283261 -id:A283261 - cp's OEIS frontend

A070861 Triangle of all possible distinct numbers obtained as a product of distinct numbers from 1..n.

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

Amarnath Murthy, May 16 2002

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

			Triangle begins:
  1;
  1;
  1, 2;
  1, 2, 3, 6;
  1, 2, 3, 4, 6, 8, 12, 24;
  ...

Reinhard Zumkeller, Rows n = 0..20 of triangle, flattened

Cf. A000142, A060957.
Row sums give A070863.
Row products give A283261.

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

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

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

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

T(n,A060957(n)) = A000142(n) = n!. - Alois P. Heinz, Aug 01 2022

Corrected and extended by Lior Manor, May 23 2002

Row n=0 prepended by Alois P. Heinz, Aug 01 2022

A283260 Product of the products of elements of all the nonempty subsets of the sets of numbers from 1 to n.

Original entry on oeis.org

1, 4, 1296, 110075314176, 1848842588950364160000000000000000, 27204445973673520186989292010512474445356561349778469394841600000000000000000000000000000000

Offset: 1

Jaroslav Krizek, Mar 04 2017

a(7) has 237 digits.

			Rows with nonempty subsets of the sets of numbers from 1 to n:
{1};
{1}, {2}, {1, 2};
{1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3};
...
Rows with the products of elements of these subsets:
1;
1, 2, 2;
1, 2, 3, 2, 3, 6, 6;
...
a(1) = (1), a(2) = (1*2*2) = 4, a(3) = (1*2*3*2*3*6*6) = 1296, ...

N. J. A. Sloane, Table of n, a(n) for n = 1..8

Cf. A000225, A001788, A033312, A067174, A229338, A283261.

a(n)=n!^2^(n-1) \\ Charles R Greathouse IV, Mar 06 2017

a(n) = (n!)^(2^(n-1)).

cp's OEIS Frontend

A070861 Triangle of all possible distinct numbers obtained as a product of distinct numbers from 1..n.

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