Sums of Quotients of Additive Functions
Sums of Quotients of Additive Functions
Denote by $\omega (n)$ and $\Omega (n)$ the number of distinct prime factors of $n$ and the total number of prime factors of $n$, respectively. Given any positive integer $\alpha$, we prove that \[ \sum \limits _{2 \leqq n \leqq x} {\Omega (n)/\omega } (n) = x + x\sum \limits …