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%I #22 Dec 07 2020 11:34:55
%S 1,2,3,4,5,7,9,11,13,16,17,19,23,25,29,31,37,41,43,47,49,53,59,61,67,
%T 71,73,79,81,83,89,97,101,103,107,109,113,121,127,128,131,137,139,149,
%U 151,157,163,167,169,173,179,181,191,193,197,199,210,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,289,293,307,311,313,317,331
%N a(1) = 1, a(2) = 2, a(3) = 3 and a(n) is the smallest number such that all a(i)*a(j)*a(k) are different.
%C Note that a(57) = 210 = 2*3*5*7, while 330 = 2*3*5*11 is not in the sequence. This demonstrates that this sequence is not determined by prime signature alone. - _Charles R Greathouse IV_, Oct 17 2015
%H Zak Seidov, <a href="/A079852/b079852.txt">Table of n, a(n) for n = 1..200</a>
%t f[l_List] := Block[{k = 1,p2 = Times @@@ Subsets[l, {2}], p3 = Times @@@ Subsets[l, {3}]},While[Intersection[p3, p2*k] != {}, k++ ]; Append[l, k]]; Nest[f, {1, 2, 3}, 62] (* _Ray Chandler_, Feb 12 2007 *)
%Y Cf. A000045, A079850, A066720, A026477.
%K nonn
%O 1,2
%A _Amarnath Murthy_, Feb 19 2003
%E Extended by _Ray Chandler_, Feb 12 2007
%E Typo in name fixed by _Zak Seidov_, Jul 06 2013