On a Problem of Erd?s Involving the Largest Prime Factor of n

Let P(n) denote the largest prime factor of an integer n (N(x) = x (2+O(?{log₂ x/logx} ) )ò₂^xr(logx/logt) (logt)/(t²)] d t,N(x) = x \left(2+O\left(\sqrt{\log_{2}\,x/\!\log x}\,\right) \right)\int_2^x\rho(\log x/\!\log t) {\log t\over t^2} {\rm d} t,