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%I #12 Sep 16 2017 00:33:27
%S 1,209,1121,2989,11381,34889,47701,62453,188785,878185,1761737,
%T 3931385,5630905,7990481,32892077,204570037,253223785,1353794333,
%U 2877954833
%N Sequence starting with 1 such that the sum of any two distinct elements has four distinct prime factors.
%C Choose the first number not leading to a contradiction.
%e Each of the three pairwise sums of the subset {1, 209, 1121} is the product of four distinct prime factors: {2*3*5*7, 2*3*11*17, 2*3*5*137}.
%p with(numtheory):nn:=100000:T:=array(1..nn): U:=array(1..nn): for p from 1 to
%p nn do: T[p]:=p:U[p]:=1:od:for u from 1 to 30 do: k:=1+u:for n from u+1 to nn
%p do:s:=T[n]+T[u]:s1:=nops(factorset(s)):s2:=bigomega(s):if s1=4 and s2=4 then
%p U[k]:=T[n]:k:=k+1:else fi:od:for i from 1 to nn do:T[i]:=U[i]:od:od:for j from
%p 1 to 30 do:printf(`%d, `, T[j]):od:
%Y Cf. A180514, A180565, A180615, A181620, A181622.
%K nonn
%O 1,2
%A _Michel Lagneau_, Jan 31 2011
%E a(9)-a(19) from _Donovan Johnson_, Feb 14 2011
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