I am interested in the rate of decay of the sum

$$\sum_{n=N}^{\infty}\frac{\phi(n)}{n^{s}}$$
where $\phi$ is Euler's totient function and $s>2$ (in which case the sum converges trivially).

Of course there's the trivial bound $\sum_{n=N}^{\infty}\frac{\phi(n)}{n^{s}}\leq\sum_{n=N}^{\infty}\frac{1}{n^{s-1}}\leq C(s)\frac{1}{N^{s-2}}$.

I'm wondering if it's possible to do any better.