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507. Perfect Number

Description

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.

Given an integer n, return true if n is a perfect number, otherwise return false.

 

Example 1:

Input: num = 28
Output: true
Explanation: 28 = 1 + 2 + 4 + 7 + 14
1, 2, 4, 7, and 14 are all divisors of 28.

Example 2:

Input: num = 7
Output: false

 

Constraints:

  • 1 <= num <= 108

Solutions

Solution 1: Enumeration

First, we check if \(\textit{num}\) is 1. If it is, then \(\textit{num}\) is not a perfect number, and we return \(\text{false}\).

Next, we enumerate all positive divisors of \(\textit{num}\) starting from 2. If \(\textit{num}\) is divisible by a positive divisor \(i\), we add \(i\) to the sum \(\textit{s}\). If the quotient of \(\textit{num}\) divided by \(i\) is not equal to \(i\), we also add the quotient to the sum \(\textit{s}\).

Finally, we check if \(\textit{s}\) is equal to \(\textit{num}\).

The time complexity is \(O(\sqrt{n})\), where \(n\) is the value of \(\textit{num}\). The space complexity is \(O(1)\).

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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

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class Solution {
    public boolean checkPerfectNumber(int num) {
        if (num == 1) {
            return false;
        }
        int s = 1;
        for (int i = 2; i <= num / i; ++i) {
            if (num % i == 0) {
                s += i;
                if (i != num / i) {
                    s += num / i;
                }
            }
        }
        return s == num;
    }
}

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class Solution {
public:
    bool checkPerfectNumber(int num) {
        if (num == 1) {
            return false;
        }
        int s = 1;
        for (int i = 2; i <= num / i; ++i) {
            if (num % i == 0) {
                s += i;
                if (i != num / i) {
                    s += num / i;
                }
            }
        }
        return s == num;
    }
};

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func checkPerfectNumber(num int) bool {
    if num == 1 {
        return false
    }
    s := 1
    for i := 2; i <= num/i; i++ {
        if num%i == 0 {
            s += i
            if j := num / i; i != j {
                s += j
            }
        }
    }
    return s == num
}

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function checkPerfectNumber(num: number): boolean {
    if (num <= 1) {
        return false;
    }
    let s = 1;
    for (let i = 2; i <= num / i; ++i) {
        if (num % i === 0) {
            s += i;
            if (i * i !== num) {
                s += num / i;
            }
        }
    }
    return s === num;
}

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