<section id="description">

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 }.
We define F(N) as the number of permutations of S(N) in which each element comes after all of its proper divisors.
This is one of the possible permutations for N = 20.
<ul>
<li>1, 2, 4, 3, 9, 8, 16, 6, 18, 12.</li>
</ul>
This is not a valid permutation because 12 comes before its divisor 6.
<ul>
<li>1, 2, 4, 3, 9, 8, 12, 16, 6, 18.</li>
</ul>
We can verify that F(6) = 5, F(8) = 9, F(20) = 450 and F(1000) ≈ 8.8521816557e21.
Find F(1018). Give as your answer 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.
</section>

function euler462() {
  // Good luck!
  return true;
}

euler462();


index

Задача 462: Перестановка 3-гладких чисел

Problem 462: Permutation of 3-smooth numbers

<code>euler462()</code> should return Infinity.