7d9496e52c
* fix: clean-up Project Euler 361-380 * fix: improve wording Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> * fix: remove unnecessary paragraph * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
53 lines
1008 B
Markdown
53 lines
1008 B
Markdown
---
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id: 5900f4d61000cf542c50ffe9
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title: 'Problem 362: Squarefree factors'
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challengeType: 5
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forumTopicId: 302023
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dashedName: problem-362-squarefree-factors
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---
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# --description--
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Consider the number 54.
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54 can be factored in 7 distinct ways into one or more factors larger than 1:
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$$54, 2 × 27, 3 × 18, 6 × 9, 3 × 3 × 6, 2 × 3 × 9 \text{ and } 2 × 3 × 3 × 3$$
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If we require that the factors are all squarefree only two ways remain: $3 × 3 × 6$ and $2 × 3 × 3 × 3$.
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Let's call $Fsf(n)$ the number of ways $n$ can be factored into one or more squarefree factors larger than 1, so $Fsf(54) = 2$.
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Let $S(n)$ be $\sum Fsf(k)$ for $k = 2$ to $n$.
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$S(100) = 193$.
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Find $S(10\\,000\\,000\\,000)$.
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# --hints--
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`squarefreeFactors()` should return `457895958010`.
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```js
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assert.strictEqual(squarefreeFactors(), 457895958010);
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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 squarefreeFactors() {
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return true;
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}
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squarefreeFactors();
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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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