Bateman-Horn conjecture, continued The Galois group acts transitively on the roots, and Burnside's lemma gives that the average number of fixed points is the size of the orbit which is one.

Table of LCM's vs. table of products I think there'll be about as many numbers of the form lcm$(a,b)$. Ford counts integers having a divisor in an interval $[y,2y]$, and one should be able to adapt this to counting square-free integers with such a divisor. Of course, a square-free integer in the multiplication table arises also as lcm$(a,b)$.