## Coresilience

### Problem 245

Published on Friday, 15th May 2009, 02:00 pm; Solved by 508

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 21011, for which C(n) is a unit fraction.