%I A064765
%S A064765 1,2,5,6,12,17,21,22,26,29,33,39,40,46,51,53,56,57,66,73,77,85,86,89,97,
%T A064765 101,102,106,114,117,131,133,134,135,137,141,146,149,151,161,165,166,
%U A064765 176,177,181,182,197,201,202,206,209,211,214,221,229,231,237,241,246
%N A064765 a(n) is the smallest number such that for, all m<n, both a(n)*a(m) and 
               a(n)+a(m) are non-squares.
%C A064765 No number occurs more than once in the sequence because if a(n)=m then 
               if m occurs again then a(n)*m=m^2. a(n) is always bigger then a(n-1) 
               because all numbers less than a(n-1) have been checked to see if 
               they make a square and if any do then because of the uniqueness of 
               each value of a(n) then they must have already occurred in the sequence 
               previously.
%e A064765 a(4) = 6 because a(1)*6 = 6, a(2)*6 = 12, a(3)*6 = 30 and a(1)+6 = 7, 
               a(2)+6 = 8, a(3)+6=11, all non-squares
%Y A064765 Sequence in context: A085206 A058601 A108365 this_sequence A082552 A057683 
               A069480
%Y A064765 Adjacent sequences: A064762 A064763 A064764 this_sequence A064766 A064767 
               A064768
%K A064765 nonn
%O A064765 1,2
%A A064765 Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Oct 18 2001