a2b2ef3f75
* fix: clean-up Project Euler 441-460 * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
49 lines
852 B
Markdown
49 lines
852 B
Markdown
---
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id: 5900f52c1000cf542c51003f
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title: 'Problem 448: Average least common multiple'
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challengeType: 5
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forumTopicId: 302120
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dashedName: problem-448-average-least-common-multiple
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---
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# --description--
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The function $lcm(a, b)$ denotes the least common multiple of $a$ and $b$.
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Let $A(n)$ be the average of the values of $lcm(n, i)$ for $1 ≤ i ≤ n$.
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E.g: $A(2) = \frac{2 + 2}{2} = 2$ and $A(10) = \frac{10 + 10 + 30 + 20 + 10 + 30 + 70 + 40 + 90 + 10}{10} = 32$.
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Let $S(n) = \sum A(k)$ for $1 ≤ k ≤ n$.
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$S(100) = 122\\,726$.
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Find $S(99\\,999\\,999\\,019)\bmod 999\\,999\\,017$.
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# --hints--
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`averageLCM()` should return `106467648`.
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```js
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assert.strictEqual(averageLCM(), 106467648);
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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 averageLCM() {
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return true;
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}
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averageLCM();
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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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