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| id | title | challengeType | forumTopicId | dashedName |
|---|---|---|---|---|
| 5900f4621000cf542c50ff74 | Problem 245: Coresilience | 5 | 301892 | 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.
assert.strictEqual(coresilience(), 288084712410001);
--seed--
--seed-contents--
function coresilience() {
return true;
}
coresilience();
--solutions--
// solution required