Four Divisors — LeetCode 1390 Python Solution

The problem

Given an integer array nums, return the sum of divisors of the integers in that array that have exactly four divisors. If there is no such integer in the array, return 0.

Example

Input

nums = [21,4,7]

Output

32

Explanation

21 has 4 divisors: 1, 3, 7, 21

Python solution

class Solution:
    def sumFourDivisors(self, nums: List[int]) -> int:
        def f(x: int) -> int:
            i = 2
            cnt, s = 2, x + 1
            while i <= x // i:
                if x % i == 0:
                    cnt += 1
                    s += i
                    if i * i != x:
                        cnt += 1
                        s += x // i
                i += 1
            return s if cnt == 4 else 0

        return sum(f(x) for x in nums)

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 1390. Four Divisors is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Math.

The math and number theory guide has the Python template for the pattern and the 485 LeetCode problems that use it.

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