# 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