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Coresilience

 Published on Friday, 15th May 2009, 02:00 pm; Solved by 757;
Difficulty rating: 80%

Problem 245

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 $\dfrac{\phi(d)}{d - 1}$, where φ is Euler's totient function.

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

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 fraction.