For a positive integer \(n\), define \(\phi(n)\) to be the number of positive integers \(a

(a, n)=1\). (For example, \(\phi(2)=1, \phi(3)=2, \phi(4)=\) 2.)

Work out \(\phi(n)\) for \(n=5,6, \ldots, 10\).

If \(p\) is a prime, show that \(\phi(p)=p-1\) and, more generally, that \(\phi\left(p^{r}\right)=\) \(p^{r}-p^{r-1}\).