65 lines
2.0 KiB
Markdown
65 lines
2.0 KiB
Markdown
---
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id: 5900f3b11000cf542c50fec4
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title: 'Problem 69: Totient maximum'
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challengeType: 5
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forumTopicId: 302181
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dashedName: problem-69-totient-maximum
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---
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# --description--
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Euler's Totient function, φ(`n`) \[sometimes called the phi function], is used to determine the number of numbers less than `n` which are relatively prime to `n`. For example, as 1, 2, 4, 5, 7, and 8, are all less than nine and relatively prime to nine, φ(9)=6.
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<div style='margin-left: 4em;'>
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| !!crwdBlockTags_15_sgaTkcolBdwrc!! | Relatively Prime | φ(!!crwdBlockTags_16_sgaTkcolBdwrc!!) |!!crwdBlockTags_17_sgaTkcolBdwrc!!/φ(!!crwdBlockTags_18_sgaTkcolBdwrc!!) |
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| ------------ | ---------------- | --------------- | ---------------------------- |
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| 2 | 1 | 1 | 2 |
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| 3 | 1,2 | 2 | 1.5 |
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| 4 | 1,3 | 2 | 2 |
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| 5 | 1,2,3,4 | 4 | 1.25 |
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| 6 | 1,5 | 2 | 3 |
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| 7 | 1,2,3,4,5,6 | 6 | 1.1666... |
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| 8 | 1,3,5,7 | 4 | 2 |
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| 9 | 1,2,4,5,7,8 | 6 | 1.5 |
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| 10 | 1,3,7,9 | 4 | 2.5 |
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</div>
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It can be seen that `n`=6 produces a maximum `n`/φ(`n`) for `n` ≤ 10.
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Find the value of `n` ≤ 1,000,000 for which n/φ(`n`) is a maximum.
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# --hints--
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`totientMaximum()` should return a number.
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```js
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assert(typeof totientMaximum() === 'number');
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```
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`totientMaximum()` should return 510510.
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```js
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assert.strictEqual(totientMaximum(), 510510);
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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 totientMaximum() {
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return true;
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}
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totientMaximum();
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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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