32dbe23f5e
* fix: clean-up Project Euler 301-320 * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
51 lines
1.3 KiB
Markdown
51 lines
1.3 KiB
Markdown
---
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id: 5900f49b1000cf542c50ffad
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title: 'Problem 302: Strong Achilles Numbers'
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challengeType: 5
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forumTopicId: 301956
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dashedName: problem-302-strong-achilles-numbers
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---
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# --description--
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A positive integer $n$ is powerful if $p^2$ is a divisor of $n$ for every prime factor $p$ in $n$.
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A positive integer $n$ is a perfect power if $n$ can be expressed as a power of another positive integer.
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A positive integer $n$ is an Achilles number if $n$ is powerful but not a perfect power. For example, 864 and 1800 are Achilles numbers: $864 = 2^5 \times 3^3$ and $1800 = 2^3 \times 3^2 \times 5^2$.
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We shall call a positive integer $S$ a Strong Achilles number if both $S$ and $φ(S)$ are Achilles numbers. $φ$ denotes Euler's totient function.
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For example, 864 is a Strong Achilles number: $φ(864) = 288 = 2^5 \times 3^2$. However, 1800 isn't a Strong Achilles number because: $φ(1800) = 480 = 2^5 \times 3^1 \times 5^1$.
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There are 7 Strong Achilles numbers below ${10}^4$ and 656 below ${10}^8$.
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How many Strong Achilles numbers are there below ${10}^{18}$?
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# --hints--
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`strongAchillesNumbers()` should return `1170060`.
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```js
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assert.strictEqual(strongAchillesNumbers(), 1170060);
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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 strongAchillesNumbers() {
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return true;
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}
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strongAchillesNumbers();
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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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