I've been trying to prove the following fact: If $\varphi$ denotes Euler's totient function, then for $Q\geq 1$ we have \begin{align*} \sum_{n\geq Q} \frac{1}{\varphi(n)^2} \ll Q^{-1}. \end{align*} I am able to prove that $\sum_{n\geq Q} \frac{1}{n^2} \ll Q^{-1},$ and I'm familiar with Euler products but unclear on the best way to apply them here. I am also aware of the estimate $\varphi(n)\gg n/\log (\log(n))$. Any hints would be really helpful! Do I need to use some kind of averaging argument for $\varphi?$


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