Coresilience
We shall call a fraction that cannot be cancelled 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, $R(12) = \dfrac{4}{11}$.
The resilience of a number $d \gt 1$ is then $\dfrac{\varphi(d)}{d - 1}$, where $\varphi$ is Euler's totient function.
We further define the coresilience of a number $n \gt 1$ as $C(n) = \dfrac{n - \varphi(n)}{n - 1}$.
The coresilience of a prime $p$ is $C(p) = \dfrac{1}{p - 1}$.
Find the sum of all composite integers $1 \lt n \le 2 \times 10^{11}$, for which $C(n)$ is a unit fractionA fraction with numerator $1$.