There is a cute argument (I think it is due to Erdos) that, asymptotically, 0% of the integers in [0,n^2] appears in the "n by n multiplication table":

By Erdos-Kac, almost all integers of size about n^2 have about log(log(n^2)) ~ log(log(n)) prime factors. However, almost all integers in the multiplication table have about 2*log(log(n)) prime factors.

Kevin Ford gets much more precise asymptotic estimates.