A027424 annoys me.
Yes, I agree. For the record, the sort-of complementary problem is A033677: Smallest divisor of n >= sqrt(n). Then A033677(n) is the smallest k such that n appears in the k-by-k multiplication table, and A027424(k) is the number of n with A033677(n) <= k. These seq's should probably be cross-linked to each other. I agree with Rich that maybe the first differences seem easier to attack, but this might be deceptive... this is asking how many of {n,2n,3n,...,n^2} are not ij for i,j<n, and doing this based on the factorization of n means recognizing things like "No, 34*16 isn't new for n=34, because it already appeared as 32*17." Maybe for each n you can look at its prime factorization and calculate one list of likely factor swaps to look out for? Ugh. --Michael Kleber kleber@brandeis.edu