Betrothed numbers in C Program?


Here we will see the Betrothed number. This is a pair of numbers, such that the sum of the proper divisors of one number is one more than the other number. We have to find these pairs

For an example, the pair is like (48, 75). So the divisors of 48 is {1, 2, 3, 4, 6, 8, 12, 16, 24} and sum is 76. Similarly, the divisors of 75 is {1, 3, 5, 15, 25} so sum is 49.

Algorithm

BetrothedPairs (n) −

begin
   for num in range 1 to n, do
      sum := 1
      for i in range 2 to num, do
         if num is divisible by i, then
            sum := sum + i
            if i * i is not same as num, then
               sum := sum + num / i
            end if
         end if
         if sum > num, then
            num2 := sum – 1
            sum2 := 1
            for j in range 2 to num2, do
               if num2 is divisible by j, then
                  sum2 := sum2 + j
                  if j * j is not same as num2, then
                     sum2 := sum2 + num2 / j
                  end if
               end if
            done
            if sum2 = num + 1, then
               print the pair num and num2
            end if
         end if
      done
   done
end

Example

#include <iostream>
using namespace std;
void BetrothedPairs(int n) {
   for (int num = 1; num < n; num++) {
      int sum = 1;
      for (int i = 2; i * i <= num; i++) { //go through each number to get proper divisor
         if (num % i == 0) {
            sum += i;
            if (i * i != num) //avoid to include same divisor twice
            sum += num / i;
         }
      }
      if (sum > num) {
         int num2 = sum - 1;
         int sum2 = 1;
         for (int j = 2; j * j <= num2; j++){
            if (num2 % j == 0) {
               sum2 += j;
               if (j * j != num2)
               sum2 += num2 / j;
            }
         }
         if (sum2 == num+1)
         cout << "(" << num << ", " << num2 <<")" << endl;
      }
   }
}
int main() {
   int n = 5000;
   BetrothedPairs(n);
}

Output

1
raja
Published on 20-Aug-2019 16:36:54
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