In this paper (2.1) I need to understand the formula for the total number of operations: $\sum_{i=1}^{\pi(\sqrt n)}\frac{n}{p_i} \approx n\ln \ln n + O(n)$ On a sidenote, since we're only checking up till the square root then why shouldn't the summand be $\frac{\sqrt{n}}{p_i}$
I have taken sequences and series and calculus in the past but I am clueless regarding these sums one pages 3 and 4.