The asymptotic distribution of the largest prime divisor
  We consider the Dickman function $\Psi (x,y)$ in the limit when $\ln x/\ln y\to \infty $ and $\ln \ln x \ln y\to 0$. The asymptotic value is expressed in terms of the ratio of iterated loragithm of $x$ and $ln y$. 
Arie Leizarowitz