%I #27 Aug 04 2022 05:53:25

%S 2,3,6,12,18,24,36,48,54,72,96,108,144,162,192,216,288,324,384,432,

%T 486,576,648,768,864,972,1152,1296,1458,1536,1728,1944,2304,2592,2916,

%U 3072,3456,3888,4374,4608,5184,5832,6144,6912,7776,8748,9216,10368,11664

%N a(n) is smallest number > a(n-1) of form a(i)*a(j), i < j < n.

%C Sequence contains 2, 3 and all numbers of form 2^a*3^b where a >= 1 and b >= 1. - _David W. Wilson_, Aug 15 1996

%C Main entry for this sequence is A033845, which is this sequence starting at 6. - _Charles R Greathouse IV_, Feb 27 2012

%D Amarnath Murthy, The sum of the reciprocals of the Smarandache multiplicative sequence, (to be published in Smarandache Notions Journal).

%D F. Smarandache, "Properties of the Numbers", University of Craiova Archives, 1975; Arizona State University Special Collections, Tempe, AZ

%D M. Myers, Smarandache Multiplicative Numbers, in Memorables 1998, Bristol Banner Books, Bristol, p. 37, 1998.

%H F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/Sequences-book.pdf">Sequences of Numbers Involved in Unsolved Problems</a>.

%F Sum_{n>=1} 1/a(n) = 4/3. - _Amiram Eldar_, Jul 31 2022

%t a[1] = 2; a[2] = 3; a[n_] := a[n] = For[k = a[n - 1] + 1, True, k++, If[ AnyTrue[Table[a[i] a[j], {i, 1, n-2}, {j, i+1, n-1}] // Flatten, # == k& ], Return[k]]]; Table[an = a[n]; Print[an]; an, {n, 1, 50}] (* _Jean-François Alcover_, Feb 08 2016 *)

%Y Subsequence of A003586 (3-smooth numbers).

%Y A007335 and A033845 are subsequences.

%K nonn,easy

%O 1,1

%A R. Muller

%E More terms from _David W. Wilson_, Aug 15 1996