---
id: 5900f4621000cf542c50ff74
title: 'Problem 245: Coresilience'
challengeType: 5
forumTopicId: 301892
dashedName: problem-245-coresilience
---

# --description--

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, $R(12) = \frac{4}{11}$.

The resilience of a number $d > 1$ is then $\frac{φ(d)}{d − 1}$ , where $φ$ is Euler's totient function.

We further define the coresilience of a number $n > 1$ as $C(n) = \frac{n − φ(n)}{n − 1}$.

The coresilience of a prime $p$ is $C(p) = \frac{1}{p − 1}$.

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

# --hints--

`coresilience()` should return `288084712410001`.

```js
assert.strictEqual(coresilience(), 288084712410001);
```

# --seed--

## --seed-contents--

```js
function coresilience() {

  return true;
}

coresilience();
```

# --solutions--

```js
// solution required
```