A generalization of the Dressler theorem (Q1390445)

Dressler's result \[ \sum_{\substack{ n\\ \varphi(n) \leq x}} 1 \sim {\zeta(2)\zeta(3) \over \zeta(6)} \cdot x \] is generalized to \[ \sum_{\substack{ n\\ \varphi(n) \leq x}} f(n) \sim A_f \cdot x, \] where \( f \) is any multiplicative function satisfying \( | f| \leq 1 \), for which the series \(\sum_p {1\over p} \cdot (1-f(p)) \) is convergent. The proof uses elementary arguments and some sieve estimates.