size of multiplication table

I learned multiplication tables when I was young. But I still don’t know their size. Great work of Ford shows that $|(n)cdot(n)|$ is $n^2/((log n)^delta (loglog n)^{3/2})$ up to multiplicative constants, where $delta := 1-frac{1+loglog2}{log 2}$. I wonder if the limit of the ratio exists.