Problem 245: Coresilience

FCC link

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) = 4⁄11.

The resilience of a number d > 1 is then φ(d)d − 1 , where φ is Euler's totient function. We further define the coresilience of a number n > 1 as C(n)= n − φ(n)n − 1. The coresilience of a prime p is C(p) = 1p − 1. Find the sum of all composite integers 1 < n ≤ 2×1011, for which C(n) is a unit fraction.