findNthPerfectNumberRange()

Step 1: Understand the problem

The first step in solving this problem is understanding 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 number 6 is a perfect number because its divisors are 1, 2, and 3, and their sum is 6.

function isPerfectNumber(num) {
  let sum = 0;
  for(let i = 1; i <= num/2; i++) {
    if(num % i === 0) sum += i;
  }
  return sum === num;
}

Step 2: Generate perfect numbers

To find the nth perfect number within a given range, we start by generating all the perfect numbers within that range.

function generatePerfectNumbers(from, to) {
  let perfectNumbers = [];
  for(let i = from; i <= to; i++) {
    if(isPerfectNumber(i)) perfectNumbers.push(i);
  }
  return perfectNumbers;
}

Step 3: Find nth perfect number within the range

Once we have an array of perfect numbers within the given range, we can easily find the nth perfect number. If n is more than the length of the array, it means there's no nth perfect number within the range.

function findNthPerfectNumber(n, from, to) {
  const perfectNumbers = generatePerfectNumbers(from, to);
  if(n > perfectNumbers.length) return 'No nth perfect number within the range';
  return perfectNumbers[n - 1]; 
}

Conclusion

This algorithm works, but it could be really slow if the range is large, because it checks every single number within the range. A potential improvement could be to implement an algorithm that generates perfect numbers more efficiently.