397a9f0c3e
* fix: clean-up Project Euler 462-480 * fix: missing image extension * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
59 lines
1.6 KiB
Markdown
59 lines
1.6 KiB
Markdown
---
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id: 5900f53b1000cf542c51004d
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title: 'Problem 462: Permutation of 3-smooth numbers'
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challengeType: 5
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forumTopicId: 302137
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dashedName: problem-462-permutation-of-3-smooth-numbers
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---
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# --description--
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A 3-smooth number is an integer which has no prime factor larger than 3. For an integer $N$, we define $S(N)$ as the set of 3-smooth numbers less than or equal to $N$. For example, $S(20) = \\{1, 2, 3, 4, 6, 8, 9, 12, 16, 18\\}$.
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We define $F(N)$ as the number of permutations of $S(N)$ in which each element comes after all of its proper divisors.
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This is one of the possible permutations for $N = 20$.
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- 1, 2, 4, 3, 9, 8, 16, 6, 18, 12.
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This is not a valid permutation because 12 comes before its divisor 6.
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- 1, 2, 4, 3, 9, 8, 12, 16, 6, 18.
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We can verify that $F(6) = 5$, $F(8) = 9$, $F(20) = 450$ and $F(1000) ≈ 8.8521816557e\\,21$.
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Find $F({10}^{18})$. Give as your answer as a string in its scientific notation rounded to ten digits after the decimal point. When giving your answer, use a lowercase `e` to separate mantissa and exponent. E.g. if the answer is $112\\,233\\,445\\,566\\,778\\,899$ then the answer format would be `1.1223344557e17`.
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# --hints--
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`permutationOf3SmoothNumbers()` should return a string.
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```js
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assert.strictEqual(typeof permutationOf3SmoothNumbers() === 'string');
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```
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`permutationOf3SmoothNumbers()` should return the string `5.5350769703e1512`.
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```js
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assert.strictEqual(permutationOf3SmoothNumbers(), '5.5350769703e1512');
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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 permutationOf3SmoothNumbers() {
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return true;
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}
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permutationOf3SmoothNumbers();
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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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