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nt.quantity concept – What is thought about absolute convergence of Dirichlet inverses?

Given an arithmetic duty $f$ such that the partial sums $sum_{n leq x} |f(n)|$ converge as $x$ approaches $infty$, are there any outcomes regarding the convergence properties of the succession of sums of the figure $sum_{n leq x} |f^{-1}(n)|$, the place $f^{-1}$ is the Dirichlet inverse of $f$? Are there particular, identified circumstances below which these sums will converge as nicely?

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