find-nth-perfect-number()

Step 1: Understand what a perfect number is

In number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. For example, the divisors of 6 are 1, 2 and 3 (excluding 6), and 1+2+3 equals 6, so 6 is a perfect number.

public boolean isPerfect(int num) {
   int sum = 1;
   for (int i = 2; i * i <= num; i++) {
       if (num % i==0) {
           if(i * i != num)
               sum = sum + i + num / i;
           else
               sum = sum + i;
       }
   } 
   if (sum == num && num!=1)
     return true;
    return false;
}

Step 2: Generate perfect numbers

Now that we have a function to check if a number is perfect or not, we can use this function to generate perfect numbers. We start from 1 and keep checking if a number is perfect or not. If it is, we add it to our list of perfect numbers.

public List<Integer> generatePerfectNumbers(int n) {
   List<Integer> perfectNumbers = new ArrayList<>();
   for (int i = 2; i < Integer.MAX_VALUE; i++) {
       if(isPerfect(i)) {
           perfectNumbers.add(i);
           if(perfectNumbers.size() == n)
               break;
       }
   }
   return perfectNumbers;
}

Step 3: Return the nth perfect number

Finally, we need a function findNthPerfectNumber that takes an input number n and returns the nth perfect number. This method first calls the generatePerfectNumbers method to get a list of the first n perfect numbers, and then it returns the last number from this list.

public int findNthPerfectNumber(int n) {
   List<Integer> perfectNumbers = generatePerfectNumbers(n);
   return perfectNumbers.get(n-1);
}