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# Problem 245

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) = 411.

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

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

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

Find the sum of all composite integers 1 < n ≤ 2×1011, for which C(n) is a unit fraction.