A positive integer n is said to be perfect if it is equal to the sum of its proper factors ie factors other than itself So for instance the number 28 is perfect its proper factors are 124714 and 1+2+4

Here's one possible implementation:

public static boolean isPerfect(int n) { return properFactorSum(n) == n; }

public static int properFactorSum(int n) { return properFactorSum(1, n); }

public static int properFactorSum(int k, int n) { if (n == 1) { return 0; } if (k > n / 2) { return 0; } if (n % k == 0) { return k + properFactorSum(k + 1, n); } return properFactorSum(k + 1, n); }

The isPerfect method simply checks if the sum of proper factors of n is equal to n.

The properFactorSum method is recursive and calculates the sum of proper factors of n. It does this by starting with k=1 (the first possible factor) and checking if k is a factor of n. If it is, then k is added to the sum and the method is called recursively with k+1 and n. If k is not a factor of n, the method is called recursively with k+1 and n. The base cases are when n=1 (the sum is 0) and when k is greater than n/2 (there are no more factors to check).

Note that this implementation assumes that n is positive and less than 10000, and it does not handle any errors or exceptions.