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