ee1e8abd87
* feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com>
51 lines
1.1 KiB
Markdown
51 lines
1.1 KiB
Markdown
---
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id: 5900f53d1000cf542c51004f
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title: 'Problem 464: Möbius function and intervals'
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challengeType: 5
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forumTopicId: 302139
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dashedName: problem-464-mbius-function-and-intervals
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---
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# --description--
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The Möbius function, denoted μ(n), is defined as:
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μ(n) = (-1)ω(n) if n is squarefree (where ω(n) is the number of distinct prime factors of n)
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μ(n) = 0 if n is not squarefree.
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Let P(a,b) be the number of integers n in the interval \[a,b] such that μ(n) = 1. Let N(a,b) be the number of integers n in the interval \[a,b] such that μ(n) = -1. For example, P(2,10) = 2 and N(2,10) = 4.
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Let C(n) be the number of integer pairs (a,b) such that: 1 ≤ a ≤ b ≤ n, 99·N(a,b) ≤ 100·P(a,b), and 99·P(a,b) ≤ 100·N(a,b).
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For example, C(10) = 13, C(500) = 16676 and C(10 000) = 20155319.
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Find C(20 000 000).
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# --hints--
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`euler464()` should return 198775297232878.
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```js
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assert.strictEqual(euler464(), 198775297232878);
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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 euler464() {
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return true;
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}
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euler464();
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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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