51 lines
1005 B
Markdown
51 lines
1005 B
Markdown
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---
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id: 5900f4ef1000cf542c510001
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title: 'Problem 386: Maximum length of an antichain'
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challengeType: 5
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forumTopicId: 302050
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dashedName: problem-386-maximum-length-of-an-antichain
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---
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# --description--
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Let $n$ be an integer and $S(n)$ be the set of factors of $n$.
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A subset $A$ of $S(n)$ is called an antichain of $S(n)$ if $A$ contains only one element or if none of the elements of $A$ divides any of the other elements of $A$.
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For example: $S(30) = \\{1, 2, 3, 5, 6, 10, 15, 30\\}$
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$\\{2, 5, 6\\}$ is not an antichain of $S(30)$.
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$\\{2, 3, 5\\}$ is an antichain of $S(30)$.
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Let $N(n)$ be the maximum length of an antichain of $S(n)$.
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Find $\sum N(n)$ for $1 ≤ n ≤ {10}^8$
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# --hints--
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`maximumLengthOfAntichain()` should return `528755790`.
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```js
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assert.strictEqual(maximumLengthOfAntichain(), 528755790);
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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 maximumLengthOfAntichain() {
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return true;
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}
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maximumLengthOfAntichain();
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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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