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%I #14 Dec 05 2013 19:56:53
%S 1,2,3,6,4,8,12,18,24,36,48,72,144,5,10,15,16,20,30,32,40,54,60,64,80,
%T 90,96,108,120,160,180,192,216,240,270,288,320,324,360,384,432,480,
%U 540,576,648,720,768,864,960,1080,1152,1296,1440,1536,1620,1728,1920,1944
%N a(1) = 1, a(2) = 2; then all new products of subsets of pre-existing terms, then the first integer not present, and so on.
%C Another rearrangement of the natural numbers.
%C Description: the iterative extension of the sequence is a loop over the steps: (i) Select the smallest integer not yet in the sequence and append it. (ii) Compute a set of all products of two or more distinct factors taken from the current, finite version of the sequence. (iii) Remove members from this set that are already in the sequence. Append the sorted list of the numbers in the set to the sequence. Return to (i). - _R. J. Mathar_, Feb 21 2009
%H R. J. Mathar, <a href="/A096113/b096113.txt">Table of n, a(n) for n = 1..385</a>
%e a(3) = 3 because all products of {1, 2} are already included. The only new product generated by {1, 2, 3} is 6, then 4 is the first integer which doesn't appear. Then {1, 2, 3, 6, 4} generates 8 (=2*4), 12 (=2*6=3*4), 18 (=3*6), 24 (=6*4=2*3*4), 36 (=2*3*6), 48 (=2*6*4), 72 (=3*6*4) and 144 (=2*3*6*4). Then the next term is 5. And so on.
%t L[1]={1} L[n_]:=L[n]=Join[L[n-1], Complement[Union[Exp[Map[ Total,Log[Subsets[Delete[L[n-1],1]]]]]],L[n-1]],{n}] L[6]
%Y Cf. A096111, A052330.
%K nonn
%O 1,2
%A _Amarnath Murthy_, Jun 29 2004
%E Edited by _Joel B. Lewis_, Nov 15 2006
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