Let $\beta(n)=\underset{p\mid n}\to\sum p$, $B(n)=\underset {p^\alpha\|n}\to\sum \alpha p$, $B_1(n)=\underset{p^\alpha\|n}\to\sum p^\alpha$. Sums of reciprocal of these functions are evaluated asymptotically. Asymptotic formulas for some related sums, involving the function $\Omega(n)$ and $\omega(n)$ (the number of distinct and total number of prime factors of $n$) are also derived.