检查数字是否为Triperfect数

给定一个数字$N$ 。任务是检查给定的号码是否是Triperfect号码。

Triperfect Number ：如果数字等于其除数之和的三倍，即其正除数之和的3倍，则数字为Triperfect数。

例子：

Input: N = 15
Output: false
Divisors of 15 are 1, 3, 5 and 15. Sum of 
divisors is 24 which is not equal to 3*15 i.e. 45.

Input: N = 120
Output: true
Sum of divisors is 360 i.e. 3*120.
Hence 120 is a triperfect number.

一个简单的解决方案是遍历从1到N的每个数字，并检查它是否为除数。保持所有除数之和。如果总和等于3 * N，则返回true，否则返回false。

一个有效的解决方案是遍历数字直到N的平方根。如果数字“ i”除以n，则将“ i”和n / i相加。

下面是有效方法的实现：

C++

// CPP code to check if a given 
// number is Triperfect or not 
#include
using namespace std;
  
// Returns true if n is Triperfect 
bool isTriPerfect(int n )
{
    // To store sum of divisors. 
    // Adding 1 and n since they are divisors of n.
    int sum = 1 + n;
      
    // Find all divisors and add them 
    int i = 2;
    while (i * i <= n)
    {
    if (n % i == 0)
        { 
            if (n / i == i)
                sum = sum + i;
            else
                sum = sum + i + n / i;
        }
        i += 1;
    }
      
    // If sum of divisors is equal to 
    // 3 * n, then n is a Triperfect number 
    if (sum == 3 * n and n != 1)
       return true;
    else
       false;
}
  
// Driver program 
int main()
{
 int n = 120;
  
 if (isTriPerfect(n)) 
    cout<

---

Java

// Java code to check if a given 
// number is Triperfect or not 
  
public class GFG{
      
    // Returns true if n is Triperfect 
    static boolean isTriPerfect(int n ) 
    { 
        // To store sum of divisors. 
        // Adding 1 and n since they are divisors of n. 
        int sum = 1 + n; 
          
        // Find all divisors and add them 
        int i = 2; 
        while (i * i <= n) 
        { 
        if (n % i == 0) 
            { 
                if (n / i == i) 
                    sum = sum + i; 
                else
                    sum = sum + i + n / i; 
            } 
            i += 1; 
        } 
          
        // If sum of divisors is equal to 
        // 3 * n, then n is a Triperfect number 
        if (sum == 3 * n & n != 1) 
            return true; 
        else
            return  false; 
    } 
      
    // Driver program 
    public static void main(String []args)
    { 
    int n = 120; 
      
    if (isTriPerfect(n)) 
        System.out.println(n + " is a Triperfect number");     
    } 
      
    //This code is contributed by 
    // Ryuga
}

Python3

# Python3 code to check if a given 
# number is Triperfect or not 
  
# Returns true if n is Triperfect 
def isTriPerfect( n ): 
      
    # To store sum of divisors. 
    # Adding 1 and n since they are divisors of n.
    sum = 1 + n
      
    # Find all divisors and add them 
    i = 2
    while i * i <= n: 
        if n % i == 0: 
            if n / i == i:
                sum = sum + i
            else:
                sum = sum + i + n / i 
        i += 1
      
    # If sum of divisors is equal to 
    # 3 * n, then n is a Triperfect number 
    return (True if sum == 3 * n and n != 1 else False) 
  
# Driver program 
n = 120
  
if isTriPerfect (n): 
    print(n, "is a Triperfect number")

C#

// C# code to check if a given 
// number is Triperfect or not 
using System;
public class GFG{
      
    // Returns true if n is Triperfect 
    static bool isTriPerfect(int n ) 
    { 
        // To store sum of divisors. 
        // Adding 1 and n since they are divisors of n. 
        int sum = 1 + n; 
          
        // Find all divisors and add them 
        int i = 2; 
        while (i * i <= n) 
        { 
        if (n % i == 0) 
            { 
                if (n / i == i) 
                    sum = sum + i; 
                else
                    sum = sum + i + n / i; 
            } 
            i += 1; 
        } 
          
        // If sum of divisors is equal to 
        // 3 * n, then n is a Triperfect number 
        if (sum == 3 * n & n != 1) 
            return true; 
        else
            return false; 
    } 
      
    // Driver program 
    public static void Main()
    { 
    int n = 120; 
      
    if (isTriPerfect(n)) 
        Console.WriteLine(n + " is a Triperfect number");     
    } 
      
    //This code is contributed by 
    // Mukul Singh
}

输出：

120 is a Triperfect number

有关TriPerfect Numbers的一些有趣事实：

• 到目前为止，只有6个Triperfect号码是已知的。它们是120、672、523776、459818240、1476304896和51001180160。
• 尚未证明不存在更多的Triperfect数，但据信这是仅有的六个。

同样，我们可以检查四次完美数(因数之和= 4 * n)，五次完美数(因数之和= 5 * n)等等。当前，已知36个四全数和65个五全数。