等分总和-yiteyi-C++库

在数论中 等分总和 正整数n的s（n）是n的所有真因子之和，也就是n的除n本身以外的所有因子之和。它们由等分因子之和定义。一个数的等分除数是除数本身以外的所有除数。等分之和是等分因子的和，例如，12的等分因子是1，2，3，4和6，等分之和是16。一个数字 等分总和 等于它的值是一个完美的数字（例如6）。 例如：

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Input : 12Output : 16Explanation :Proper divisors of 12 is = 1, 2, 3, 4, 6 and sum 1 + 2 + 3 + 4 + 6 = 16Input : 15Output : 9Explanation :Proper divisors of 15 is 1, 3, 5and sum 1 + 3 + 5 = 9

推荐：请尝试你的方法 {IDE} 首先，在进入解决方案之前。

A. 简单解决方案 遍历所有小于n的数。对于每个数i，检查i是否除以n。如果是，我们将其添加到结果中。

C++

                         // CPP program for aliquot sum                       
                         #include <iostream>                       
                         using                                     namespace                                     std;                       
           
                         // Function to calculate sum of                       
                         // all proper divisors                       
                         int                                     aliquotSum(                                     int                                     n)                       
                         {                       
                                                 int                                     sum = 0;                       
                                                 for                                     (                                     int                                     i = 1; i < n; i++)                       
                                                 if                                     (n % i == 0)                       
                                                 sum += i;                       
                                   
                                                 return                                     sum;                       
                         }                       
           
                         // Driver Code                       
                         int                                     main()                       
                         {                       
                                                 int                                     n = 12;                       
                                                 cout << aliquotSum(n);                       
                                                 return                                     0;                       
                         }                       

JAVA

                         // Java program for aliquot sum                       
                         import                                     java.io.*;                       
           
                         class                                     GFG {                       
                                   
                                                 // Function to calculate sum of                       
                                                 // all proper divisors                       
                                                 static                                     int                                     aliquotSum(                                     int                                     n)                       
                                                 {                       
                                                 int                                     sum =                                     0                                     ;                       
                                                 for                                     (                                     int                                     i =                                     1                                     ; i < n; i++)                       
                                                 if                                     (n % i ==                                     0                                     )                       
                                                 sum += i;                       
                                   
                                                 return                                     sum;                       
                                                 }                       
                                   
                                                 // Driver Code                       
                                                 public                                     static                                     void                                     main(String args[])                       
                                                 throws                                     IOException                       
                                                 {                       
                                                 int                                     n =                                     12                                     ;                       
                                                 System.out.println(aliquotSum(n));                       
                                                 }                       
                         }                       
           
                         /* This code is contributed by Nikita Tiwari.*/                       

Python3

                         # Python 3 program for aliquot sum                       
           
                         # Function to calculate sum of                       
                         # all proper divisors                       
                         def                                     aliquotSum(n) :                       
                                                 sm                                     =                                     0                       
                                                 for                                     i                                     in                                     range                                     (                                     1                                     ,n) :                       
                                                 if                                     (n                                     %                                     i                                     =                                     =                                     0                                     ) :                       
                                                 sm                                     =                                     sm                                     +                                     i                       
                                   
                                                 return                                     sm                                     # return sum                       
           
           
                         # Driver Code                       
                         n                                     =                                     12                       
                         print                                     (aliquotSum(n))                       
           
                         # This code is contributed by Nikita Tiwari.                       

C#

                         // C# program for aliquot sum                       
                         using                                     System;                       
           
                         class                                     GFG {                       
                                   
                                                 // Function to calculate sum of                       
                                                 // all proper divisors                       
                                                 static                                     int                                     aliquotSum(                                     int                                     n)                       
                                                 {                       
                                                 int                                     sum = 0;                       
                                                 for                                     (                                     int                                     i = 1; i < n; i++)                       
                                                 if                                     (n % i == 0)                       
                                                 sum += i;                       
                                   
                                                 return                                     sum;                       
                                                 }                       
                                   
                                                 // Driver Code                       
                                                 public                                     static                                     void                                     Main()                       
                                   
                                                 {                       
                                                 int                                     n = 12;                       
                                                 Console.WriteLine(aliquotSum(n));                       
                                                 }                       
                         }                       
           
                         /* This code is contributed by vt_m.*/                       

PHP

                         <?php                       
                         // PHP program for aliquot sum                       
           
                         // Function to calculate sum of                       
                         // all proper divisors                       
                         function                                     aliquotSum(                                     $n                                     )                       
                         {                       
                                                 $sum                                     = 0;                       
                                                 for                                     (                                     $i                                     = 1;                                     $i                                     <                                     $n                                     ;                                     $i                                     ++)                       
                                                 if                                     (                                     $n                                     %                                     $i                                     == 0)                       
                                                 $sum                                     +=                                     $i                                     ;                       
                                   
                                                 return                                     $sum                                     ;                       
                         }                       
           
                         // Driver Code                       
                         $n                                     = 12;                       
                         echo                                     (aliquotSum(                                     $n                                     ));                       
           
                         // This code is contributed by Ajit.                       
                         ?>                       

Javascript

                         <script>                       
           
                         // JavaScript program for aliquot sum                       
           
                         // Function to calculate sum of                       
                         // all proper divisors                       
                                                 function                                     aliquotSum(n)                       
                                                 {                       
                                                 let sum = 0;                       
                                                 for                                     (let i = 1; i < n; i++)                       
                                                 if                                     (n % i == 0)                       
                                                 sum += i;                       
                                   
                                                 return                                     sum;                       
                                                 }                       
                                   
           
                         // Driver code                       
                                   
                                                 let n = 12;                       
                                                 document.write(aliquotSum(n));                       
                                   
                         </script>                       

输出：

高效的解决方案： 一个自然数的所有真因子之和一个数的所有因子之和

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