Abstract
Given an additive function f and a multiplicative function g, let E(f, g;x) = #{n ≤ x: f(n) = g(n)}. We study the size of E(ω,g;x) and E(Ω,g;x), where ω(n) stands for the number of distinct prime factors of n and Ω(n) stands for the number of prime factors of n counting multiplicity. In particular, we show that E(ω,g;x) and E(Ω,g;x) are
O
x
log
log
x
$\begin{array}{}
\displaystyle
O\left(\frac{x}{\sqrt{\log\log x}}\right)
\end{array}$
for any integer valued multiplicative function g. This improves an earlier result of De Koninck, Doyon and Letendre.