1.6 KiB
id | challengeType | title |
---|---|---|
5900f4b91000cf542c50ffcc | 5 | Problem 333: Special partitions |
Description
Let's consider only those such partitions where none of the terms can divide any of the other terms. For example, the partition of 17 = 2 + 6 + 9 = (21x30 + 21x31 + 20x32) would not be valid since 2 can divide 6. Neither would the partition 17 = 16 + 1 = (24x30 + 20x30) since 1 can divide 16. The only valid partition of 17 would be 8 + 9 = (23x30 + 20x32).
Many integers have more than one valid partition, the first being 11 having the following two partitions. 11 = 2 + 9 = (21x30 + 20x32) 11 = 8 + 3 = (23x30 + 20x31)
Let's define P(n) as the number of valid partitions of n. For example, P(11) = 2.
Let's consider only the prime integers q which would have a single valid partition such as P(17).
The sum of the primes q <100 such that P(q)=1 equals 233.
Find the sum of the primes q <1000000 such that P(q)=1.
Instructions
Tests
tests:
- text: <code>euler333()</code> should return 3053105.
testString: assert.strictEqual(euler333(), 3053105, '<code>euler333()</code> should return 3053105.');
Challenge Seed
function euler333() {
// Good luck!
return true;
}
euler333();
Solution
// solution required