public class BigRationalFindPerfectNumbers {
    public static void main(String[] args) {
        int MAX_NUM = 1 << 19;
        System.out.println("Searching for perfect numbers in the range [1, " + (MAX_NUM - 1) + "]");

        BigRational TWO = BigRational.valueOf(2);
        for (int i = 1; i < MAX_NUM; i++) {
            BigRational reciprocalSum = BigRational.ONE;
            if (i > 1)
                reciprocalSum = reciprocalSum.add(BigRational.valueOf(i).reciprocal());
            int maxDivisor = (int) Math.sqrt(i);
            if (maxDivisor >= i)
                maxDivisor--;

            for (int divisor = 2; divisor <= maxDivisor; divisor++) {
                if (i % divisor == 0) {
                    reciprocalSum = reciprocalSum.add(BigRational.valueOf(divisor).reciprocal());
                    int dividend = i / divisor;
                    if (divisor != dividend)
                        reciprocalSum = reciprocalSum.add(BigRational.valueOf(dividend).reciprocal());
                }
            }
            if (reciprocalSum.equals(TWO))
                System.out.println(String.valueOf(i) + " is a perfect number");
        }
    }
}
