## 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
$\begin{array}{}{\displaystyle O\left(\frac{x}{\sqrt{\mathrm{log}\mathrm{log}x}}\right)}\end{array}$
for any integer valued multiplicative function *g*. This improves an earlier result of De Koninck, Doyon and Letendre.

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