 Resilience of a denominator

For an integer $d>1$, the proportion of proper fractions $1/d,\dots ,(d-1)/d$ already in lowest terms. There are $\phi (d)$ such fractions, so $R(d)=\phi (d)/(d-1)$. The prime factorization of $d$ gives $R(d)=\frac{d}{d-1}{\prod }_{p\mid d}(1-1/p)$.