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%I #13 Mar 16 2017 11:57:04
%S 4,4,6,4,6,9,4,6,9,10,4,6,9,10,15,4,6,9,10,15,25,4,6,9,10,14,15,21,4,
%T 6,9,10,14,15,21,25,4,6,9,10,14,15,21,25,35,4,6,9,10,14,15,21,25,35,
%U 49,4,6,9,10,14,15,21,22,25,33,35,4,6,9,10,14,15,21,22,25,33,35,49,4,6,9,10
%N Triangle in which the n-th row contains n distinct composite numbers with the least product and has least number of prime divisors. No member of a row is a multiple of another member of the row.
%C If there are two sets of distinct composite numbers satisfying the above condition then the set with lesser product is chosen irrespective of the number of prime divisors. Perhaps the ambiguity may not arise. E.g., row 6 is 4,6,9,10,15,25. This row cannot be extended to get the next row without bringing in another prime because every number divisible by 2,3 or 5 will be a multiple of one of the previous terms. Hence in row 7, prime 7 has to be brought in and then we get a new set of numbers: 4,6,9,10,14,15,21.
%e 4;
%e 4,6;
%e 4,6,9;
%e 4,6,9,10;
%e 4,6,9,10,15;
%e 4,6,9,10,15,25;
%e 4,6,9,10,14,15,21;
%Y Cf. A001358, A005843, A077554, A077555, A087112.
%K nonn,tabl
%O 0,1
%A _Amarnath Murthy_, Nov 10 2002
%E More terms from _Ray Chandler_, Aug 21 2003
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