## Coresilience

### Problem 245

Published on Friday, 15th May 2009, 02:00 pm; Solved by 530; Difficulty rating: 80%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) |
= | 1 p − 1 | . |

Find the sum of all **composite** integers 1 < `n` ≤ 2×10^{11}, for which `C`(`n`) is a unit fraction.