Resilience of a denominator
= Resilience of a denominator
{title2=$R(d)$}
= Resilience
{synonym}
For an <integer> $d>1$, the proportion of proper fractions $1/d,\ldots,(d-1)/d$ already in lowest terms. There are $\varphi(d)$ such fractions, so $R(d)=\varphi(d)/(d-1)$. The <prime factorization> of $d$ gives $R(d)=\frac d{d-1}\prod_{p\mid d}(1-1/p)$.