1.6 KiB
1.6 KiB
id | challengeType | title |
---|---|---|
5900f53b1000cf542c51004d | 5 | Problem 462: Permutation of 3-smooth numbers |
Description
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.
- 1, 2, 4, 3, 9, 8, 16, 6, 18, 12. This is not a valid permutation because 12 comes before its divisor 6.
- 1, 2, 4, 3, 9, 8, 12, 16, 6, 18.
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.
Instructions
Tests
tests:
- text: <code>euler462()</code> should return Infinity.
testString: assert.strictEqual(euler462(), Infinity, '<code>euler462()</code> should return Infinity.');
Challenge Seed
function euler462() {
// Good luck!
return true;
}
euler462();
Solution
// solution required