Perfect Number — LeetCode 507 Python Solution

The problem

A perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. A divisor of an integer x is an integer that can divide x evenly.

Example

Input

num = 28

Output

true

Explanation

28 = 1 + 2 + 4 + 7 + 14

Python solution

class Solution:
    def checkPerfectNumber(self, num: int) -> bool:
        if num == 1:
            return False
        s, i = 1, 2
        while i <= num // i:
            if num % i == 0:
                s += i
                if i != num // i:
                    s += num // i
            i += 1
        return s == num

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 507. Perfect Number 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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