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- Project Euler #245: Coresilience

# Project Euler #245: Coresilience

# Project Euler #245: Coresilience

_{This problem is a programming version of Problem 245 from projecteuler.net}

We shall call a fraction that cannot be cancelled down a **resilient** fraction.

Furthermore we shall define the **resilience** of a denominator,
, to be the ratio of its proper fractions that are resilient; for example, consider . The proper fractions with a
denominator are . Four of these cannot be
cancelled down, so the resilience is
.

The resilience of a number is then

We further define the

**coresilience**of a number as

Given an integer , find the sum of all integers for which is a unit fraction, that is, a fraction with a numerator of after cancelling down.

**Input Format**

Each test file contains a single line containing a single integer .

**Constraints**

**Output Format**

Print the integer value of the sum of all integers for which is a unit fraction.

**Sample Input 0**

```
5
```

**Sample Output 0**

```
10
```

**Explanation 0**

Integer | 2 | 3 | 4 | 5 |
---|---|---|---|---|

Euler Phi | 1 | 2 | 2 | 4 |

Coresilience | 1/1 | 1/2 | 2/3 | 1/4 |

The sum of integers with Coresilience a unit fraction: .