In order to calculate the number of pair $(a,b)$ such that $a,b \in \{1,2,\dots ,n\}$ and $a\mid b$, I want to calculate: $$f(n)=\sum_{i=1}^{n}\lfloor n/i \rfloor$$
Is there any (mathematical) way to calculate above function for example for $n=10^{100}$?