Two asymptoticd on sums of consecutive Euler's totient function.

Question

in "Two remarks on iterates of Euler's totient function" Paul Pollack on page 2 writes that:

$$\sum_{n=1}^x \phi(n) \sim \frac{3x^2}{\pi^2}$$ and

$$\sum_{n=1}^x \frac{1}{\phi(n)} \sim \frac{\zeta{(2)}\zeta{(3)}\log{x}}{\zeta{(6)}}$$

where $\phi$ is Euler function, $\zeta$ is Riemann's $\zeta$-function and $\log$ is natural logarithm.

Where can I read at least sketches of proofs of these things? The author does not give reference, only writes it is 'well-known'.

Thanks in advance for help.

Answer 1

Introduction to Analytic Number Theory Math 531 Lecture Note, Fall 2005

Is a good resource, the first one of your problems is proven within the book, the second one have a lot of hints and walkthrough without a proof but you can manage.