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 \[\begin{equation} \left\lbrace \begin{array}{ccc} p+q = n \\ 0<\frac{p}{q}<1 \\ \gcd(p,q)=1. \end{array}\right. \end{equation}\] 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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