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Given a multiplicative function $f$, is there any general method of getting a upper bound of $\sum^{'}_{n<x} f(n)$, where the sum is restricted to all those non-square-free $n$?

For example, when the sum is restricted to square-free numbers, we have $\sum^{''}_{n<x} f(n)<\prod_{p<x}(1+f(p))$. Usually by the formula $\prod_{p<x}(1+1/p)\ll\log x$ we can get the thing we want.

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