7. Amicable numbers

Two numbers are said to be amicable if the sum of the proper pisors of one number is equal to that of the other number. The proper pisors of a number are the positive prime factors of the number other than the number itself. Amicable numbers should not be confused with friendly numbers. For instance, the number 220 has the proper pisors 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, and 110, whose sum is 284. The proper pisors of 284 are 1, 2, 4, 71, and 142; their sum is 220. Therefore, the numbers 220 and 284 are said to be amicable.

The solution to this problem is to iterate through all the numbers up to the given limit. For each number, compute the sum of its proper pisors. Let’s call this sum1. Repeat the process and compute the sum of the proper pisors of sum1. If the result is equal to the original number, then the number and sum1 are amicable numbers:

void print_amicables(int const limit)
{
   for (int number = 4; number < limit; ++number)
   {
      auto sum1 = sum_proper_pisors(number);
      if (sum1 < limit)
      {
         auto sum2 = sum_proper_pisors(sum1);
         if (sum2 == number && number != sum1)
         {
            std::cout << number << "," << sum1 << std::endl;
         }
      }
   }
}

In the above sample, sum_proper_pisors() is the function seen in the solution to the abundant numbers problem.

The above function prints pairs of numbers twice, such as 220,284 and 284,220. Modify this implementation to only print each pair a single time.