1.1 KiB
1.1 KiB
| id | title | challengeType | forumTopicId | dashedName |
|---|---|---|---|---|
| 5900f4421000cf542c50ff55 | Problem 214: Totient Chains | 5 | 301856 | problem-214-totient-chains |
--description--
Let φ be Euler's totient function, i.e. for a natural number n, φ(n) is the number of k, 1 ≤ k ≤ n, for which gcd(k,n) = 1.
By iterating φ, each positive integer generates a decreasing chain of numbers ending in 1. E.g. if we start with 5 the sequence 5,4,2,1 is generated. Here is a listing of all chains with length 4:
\begin{align}
5,4,2,1 & \\\\
7,6,2,1 & \\\\
8,4,2,1 & \\\\
9,6,2,1 & \\\\
10,4,2,1 & \\\\
12,4,2,1 & \\\\
14,6,2,1 & \\\\
18,6,2,1 &
\end{align}$$
Only two of these chains start with a prime, their sum is 12.
What is the sum of all primes less than $40\\,000\\,000$ which generate a chain of length 25?
# --hints--
`totientChains()` should return `1677366278943`.
```js
assert.strictEqual(totientChains(), 1677366278943);
```
# --seed--
## --seed-contents--
```js
function totientChains() {
return true;
}
totientChains();
```
# --solutions--
```js
// solution required
```