I actually did that overkill (even though we are limited to ints instead of even longs).

    public int divisorSum (int N){
        HashMap<Integer,Integer> primeFactorization = factor(N);
        int total = 1;
        for (int p:primeFactorization.keySet()) {
            System.err.println("considering prime: " +p + " with mult: "+ primeFactorization.get(p));
            int factor = 1;
            for (int i=0;i<primeFactorization.get(p);i++) {
                factor*=p;
                factor+=1;
            }
            total*=factor;
        }

        return total;
    }
    private HashMap<Integer,Integer> factor(int n){
        HashMap<Integer,Integer> mii = new HashMap<>();
        if(isPrime(n)){
            mii.put(n,1);
            return mii;
        }
        if (n%2==0){ 
            int m = n;
            int cnt=0;
            do{
                m/=2;
                cnt++;
            }while(m%2==0);
            mii.put(2,cnt);
        }
        double ceil = n/2.0;
        for (int i = 3; i <= ceil; i += 2) {
            if ((isPrime(i)) && (n%i == 0)) {
                int m = n;
                int cnt=0;
                do{
                    m/=i;
                    cnt++;
                }while(m%i==0);
                mii.put(i,cnt);
            }
        }
        return mii;
    }

    private static boolean isPrime(int num) {
        if (num < 2) return false;
        if (num == 2) return true;
        if (num % 2 == 0) return false;
        for (int i = 3; i * i <= num; i += 2)
            if (num % i == 0) return false;
        return true;
    }