Asymptotic of some sums

The paper compares the asymptotic of the expressions $\frac {1} {x} \sum\limits_{n \leq x} {f(n)}$and$\sum\limits_{n \leq x} {\frac {f(n)} {n}}$,$\frac {1} {x} \sum\limits_{p \leq x} {f(p)}$and$\sum\limits_{p \leq x} {\frac {f(p)} {p}}$\mathrm{.}Theasymptoticofsums$\sum\limits_{n \leq x} {\frac {f(n)} {n}}$and$\sum\limits_{p \leq x} {\frac {f(p)} {p}}$($n,p$ - respectively, positive and prime numbers) are determined if the asymptotic of sums are known, respectively: $\sum _{n\le x}f(n)$,$\sum\limits_{p \leq x} {f(p)}$.