Is $a_n=\frac{1}{n}\sum_{k=1}^n\frac{\varphi(k)}{k}$ convergent? Let $(a_n)_{n\in\mathbb{N}}$ be defined as $a_n=\frac{1}{n}\sum_{k=1}^n\frac{\varphi(k)}{k}$ where $\varphi$ is the euler totient function. Is $(a_n)$ convergent. If so, what is its limit?
I have checked it numerically; it seems to converge to the value
$$
a\approx 0.6079384135652464404586775568799731914204890312331725
$$
However, I cannot think of a way to prove it.

Here you can find that the value you're looking for is $ \frac{6}{\pi^2} $
