Let $ f: \mathbb{N} \rightarrow \mathbb{N} $ be a function from the positive integers to the positive integers for which $ f(1)=1,f(2n)=f(n) $ and $ f(2n+1)=f(n)+f(n+1) $ for all $ n\in \mathbb{N} $. Prove that for any natural number $ n $, the number of odd natural numbers $ m $ such that $ f(m)=n $ is equal to the number of positive integers not greater than $ n $ having no common prime factors with $ n $.