48 lines
924 B
Markdown
48 lines
924 B
Markdown
---
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id: 5900f50f1000cf542c510021
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title: 'Problem 418: Factorisation triples'
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challengeType: 5
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forumTopicId: 302087
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dashedName: problem-418-factorisation-triples
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---
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# --description--
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Let $n$ be a positive integer. An integer triple ($a$, $b$, $c$) is called a factorisation triple of $n$ if:
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- $1 ≤ a ≤ b ≤ c$
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- $a \times b \times c = n$.
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Define $f(n)$ to be $a + b + c$ for the factorisation triple ($a$, $b$, $c$) of $n$ which minimises $\frac{c}{a}$. One can show that this triple is unique.
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For example, $f(165) = 19$, $f(100\\,100) = 142$ and $f(20!) = 4\\,034\\,872$.
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Find $f(43!)$.
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# --hints--
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`factorisationTriples()` should return `1177163565297340400`.
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```js
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assert.strictEqual(factorisationTriples(), 1177163565297340400);
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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 factorisationTriples() {
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return true;
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}
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factorisationTriples();
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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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