Problem 1. Let $d(k)$ denote the number of divisors of $k\in\mathbb{N}$. Prove that: $\sum_{k=1}^{n}d(k)=n\ln n +O(n)$
Problem 2. Show estimation below: $\sum_{k=1}^{n}\phi(k)=\frac{3}{\pi^2}\cdot n^2+O(n\log n)$ where $\phi$ is Euler's totient function of course.
I just started having fun with asymptotics and can't manage with these two. They seem very interesting, because this is the first time I've seen asymptotics and number theory together (I know, I haven't seen too much of math, yet) and I'm very curious how these problems can be solved. They also made me wonder if is there any asymptotic estimation for sum with another interesting function: $\sum_{k=1}^{n}\sigma(k)$, where $\sigma(k)$ is the sum of divisors of $k$?