The sum of the numbers of all divisors of a natural number.

Question

For natural number $n$, let $f(n)$be the number of all positive divisors of $n$.($f(1)=1,f(2)=2,f(6)=4,$etc).
Prove : $\sum^{n}_{k=1}f(k)=\sum^{n}_{k=1}\lfloor \frac{n}{k}\rfloor$.
The book this was on mentions the use of intersecting points(coordinates with only integers ex.(1,2),(3,4)). I’ve tried to visualize the right hand side of the equation like below.
The right hand side is the number of all intersecting points within the region surrounded by $y=\frac{n}{x}, y=1,x=1,x=k$,including the boundaries.
I don’t know what to do next, and I have no idea how the both sum would equal each other. Could anybody help?