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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 $\sum\limits_{p \leq x}{\frac {f(p)} {p}}$. The asymptotic of sums $\sum\limits_{n \leq x} {\frac{f(n)} {n}}$ and $\sum\limits_{p \leq x} {\frac {f(p)} {p}}$ ($n,p$ -respectively, positive and prime numbers) are determined if the asymptotic ofsums are known, respectively: $\sum\limits_{n \leq x} {f(n)}$,$\sum\limits_{p\leq x} {f(p)}$.

Asymptotic of some sums