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) = ^{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` 210^{11}, for which `C`(`n`) is a unit fraction.

**
These problems are part of
Project Euler
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