A positive fraction whose numerator is less than its denominator is called a proper fraction.
For any denominator, $d$, there will be $d−1$ proper fractions; for example, with $d = 12$:
$$\frac{1}{12}, \frac{2}{12}, \frac{3}{12}, \frac{4}{12}, \frac{5}{12}, \frac{6}{12}, \frac{7}{12}, \frac{8}{12}, \frac{9}{12}, \frac{10}{12}, \frac{11}{12}$$
We shall call a fraction that cannot be canceled down a resilient fraction.
Furthermore we shall define the resilience of a denominator, $R(d)$, to be the ratio of its proper fractions that are resilient; for example, $R(12) = \frac{4}{11}$.
In fact, $d = 12$ is the smallest denominator having a resilience $R(d) < \frac{4}{10}$.
Find the smallest denominator $d$, having a resilience $R(d) < \frac{15\,499}{94\,744}$.