49 lines
981 B
Markdown
49 lines
981 B
Markdown
---
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id: 5900f4421000cf542c50ff55
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title: 'Problem 214: Totient Chains'
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challengeType: 5
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forumTopicId: 301856
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dashedName: problem-214-totient-chains
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---
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# --description--
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Let φ be Euler's totient function, i.e. for a natural number n,
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φ(n) is the number of k, 1 ≤ k ≤ n, for which gcd(k,n) = 1.
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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:
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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
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Only two of these chains start with a prime, their sum is 12.
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What is the sum of all primes less than 40000000 which generate a chain of length 25?
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# --hints--
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`euler214()` should return 1677366278943.
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```js
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assert.strictEqual(euler214(), 1677366278943);
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```
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# --seed--
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## --seed-contents--
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```js
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function euler214() {
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return true;
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}
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euler214();
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```
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# --solutions--
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```js
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// solution required
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```
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