数学--数论--HDU 2136（素数筛选法）

Everybody knows any number can be combined by the prime number.
Now, your task is telling me what position of the largest prime factor.
The position of prime 2 is 1, prime 3 is 2, and prime 5 is 3, etc.
Specially, LPF(1) = 0.
Input
Each line will contain one integer n(0 < n < 1000000).
Output
Output the LPF(n).
Sample Input
1
2
3
4
5
Sample Output
0
1
2
1
3

#include <iostream>
#include <cmath>
#include <iomanip>
#include <algorithm>
using namespace std;
const int MAX = 1000000;
int prime[MAX];
int mark[MAX];

void init()
{
    for (int i = 2, n = 1; i < MAX; i++)
    {
        if (!prime[i])
        {
            mark[i] = n++;
            for (int j = i; j < MAX; j = j + i)
                prime[j] = i;
        }
    }
}
int main()
{
    int n;
    init();
    while (~scanf("%d", &n))
    {
        printf("%d
", mark[prime[n]]);
    }
    return 0;
}