51 lines
1.2 KiB
Markdown
51 lines
1.2 KiB
Markdown
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---
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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 p2 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 = 25·33 and 1800 = 23·32·52.
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We shall call a positive integer S a Strong Achilles number if both S and φ(S) are Achilles numbers.1 For example, 864 is a Strong Achilles number: φ(864) = 288 = 25·32. However, 1800 isn't a Strong Achilles number because: φ(1800) = 480 = 25·31·51.
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There are 7 Strong Achilles numbers below 104 and 656 below 108.
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How many Strong Achilles numbers are there below 1018?
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1 φ denotes Euler's totient function.
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# --hints--
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`euler302()` should return 1170060.
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```js
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assert.strictEqual(euler302(), 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 euler302() {
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return true;
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}
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euler302();
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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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