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, $R(12)={\displaystyle \frac{4}{11}}$.

The resilience of a number $d>1$ is then ${\displaystyle \frac{\phi (d)}{d-1}}$, where $\phi$ is Euler's totient function.

We further define the coresilience of a number $n>1$ as $C(n)={\displaystyle \frac{n-\phi (n)}{n-1}}$.

The coresilience of a prime $p$ is $C(p)={\displaystyle \frac{1}{p-1}}$.

Find the sum of all composite integers $1<n\le 2\times {10}^{11}$, for which $C(n)$ is a unit fractionA fraction with numerator $1$.