Mysterious Asymptotic Behavior 2

Let $C(N)$ be the number of positive integers $n\ge 2$ such that $n\cdot {\text{(largest prime factor of }n\text{)}}^2\le N$.

You are given that $C(10)=1,C({10}^6)=1228,C({10}^{11})=888908$ and $C({10}^{12})=3613513$.

Find $C({10}^{18})$.