Factorial Factors (UVa)

#include<bits/stdc++.h>
using namespace std;

int factor[1000000 + 5];
int cum_sum[1000000 + 5];

bool isPrime(int n) {
    for(int i = 2; i*i <= n; i++) {
        if(n % i == 0) return false;
    }
    return true;
}


int main() {
    for(int i = 2, j=1; i <= 1000000; i*=2, j++) {
        factor[i] = j;
    }
    for(int i = 3; i <= 1000000; i++) {
        if(factor[i] == 0) {
            if(isPrime(i)) {
                factor[i] = 1;
            } else {
                if(i%2 == 0) {
                    factor[i] = factor[i/2] + 1;
                } else {
                    for(int j = 3; ;j+=2) {
                        if(i % j == 0) {
                            factor[i] = factor[i/j] + 1;
                            break;
                        }
                    }
                }
            }
        }
    }
    cum_sum[2] = factor[2];
    for(int i=3; i<=1000000; i++) {
        cum_sum[i] = factor[i] + cum_sum[i-1];
    }
    int n;
    while (cin >> n) {
        cout << cum_sum[n] << endl;
    }


    return 0;
}