# Rational and Irreducible

Let $$f : \mathbb{Z}^+ \longrightarrow \mathbb{Z}^*$$ the function that assigns to each positive integer $$n$$ the number of rational numbers $$\frac{p}{q}$$ such that $$$\left\lbrace \begin{array}{ccc} p+q = n \\ 0<\frac{p}{q}<1 \\ \gcd(p,q)=1. \end{array}\right.$$$ For example, when $$n=8,$$ we have $$2$$ such rational numbers: $$\frac{1}{7}$$ and $$\frac{3}{5}$$. Hence $$f(8)=2$$.

What is the first positive integer $$m$$ such that there is no solution to $$f(n)=m?$$

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