%I #4 Apr 27 2014 09:38:46
%S 0,0,0,1,3,5,8,12,17,22,29,36,44,53,62,71,82,94,107,121,135,149,165,
%T 181,198,216,234,253,274,295,317,340,364,388,413,438,464,491,519,547,
%U 577,607,639,672,705,739,775,812,850,889,928,967,1008,1049,1090,1132,1174,1217,1262,1308
%N Number of 2element subsets of {1,...,n} whose sum has more than 3 divisors.
%C If the constraint on the number of divisors is dropped, one gets A000217 = triangular numbers n*(n+1)/2, which therefore is an upper bound.
%C If one considers 3element subsets instead, one gets A241564; see the link there for the original motivation.
%C If one considers sums with more than 2 divisors, one gets A241566.
%o (PARI) a(n,m=2,d=3)={s=0;u=vector(m,n,1)~;forvec(v=vector(m,i,[1,n]),numdiv(v*u)>d&&s++,2);s}
%K nonn
%O 1,5
%A _M. F. Hasler_, Apr 25 2014
