47 lines
1.2 KiB
Markdown
47 lines
1.2 KiB
Markdown
---
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id: 5900f4571000cf542c50ff69
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title: 'Problem 234: Semidivisible numbers'
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challengeType: 5
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forumTopicId: 301878
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dashedName: problem-234-semidivisible-numbers
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---
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# --description--
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For an integer $n ≥ 4$, we define the lower prime square root of $n$, denoted by $lps(n)$, as the $\text{largest prime} ≤ \sqrt{n}$ and the upper prime square root of $n$, $ups(n)$, as the $\text{smallest prime} ≥ \sqrt{n}$.
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So, for example, $lps(4) = 2 = ups(4)$, $lps(1000) = 31$, $ups(1000) = 37$.
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Let us call an integer $n ≥ 4$ semidivisible, if one of $lps(n)$ and $ups(n)$ divides $n$, but not both.
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The sum of the semidivisible numbers not exceeding 15 is 30, the numbers are 8, 10 and 12. 15 is not semidivisible because it is a multiple of both $lps(15) = 3$ and $ups(15) = 5$. As a further example, the sum of the 92 semidivisible numbers up to 1000 is 34825.
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What is the sum of all semidivisible numbers not exceeding 999966663333?
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# --hints--
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`semidivisibleNumbers()` should return `1259187438574927000`.
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```js
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assert.strictEqual(semidivisibleNumbers(), 1259187438574927000);
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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 semidivisibleNumbers() {
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return true;
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}
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semidivisibleNumbers();
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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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