Count Divisor in O(n^1/3)

// Count Divisor in O(n^1/3)
ll countDivisor(ll n) {
    ll ans = 1;
    int len = primeList.size();  // upto 10^6
    for (int i = 0; i < len; i++) {
        ll pNum = primeList[i];
        ll num = pNum*pNum*pNum*1LL;
        if (num > n)
            break;
        int cnt = 1;
        while (n%pNum==0) {
            n /= pNum;
            cnt++;
        }
        ans *= cnt;
    }
    ll sq = sqrt(n);
    if (isPrime(n)) //Y is prime, F(Y)=2
        ans *= 2;
    else if (sq*sq==n && isPrime(sq))  //Y is square of a prime number, F(Y)=3
        ans *= 3;
    else if (n!=1) //Y is product of two distinct prime numbers, F(Y)=4
        ans *= 4;
    return ans;
}
// 12 = 6 (1, 2, 3, 4, 6, 12)
// 999999999999999989 = 2
// 100000007700000049 = 4