素数筛模板（数学）

这是我找了好多找到素数筛优化的很不错的了  如果有大神知道还能再优化的话希望能提取宝贵意见  Orz

# include <map>
# include <queue>
# include <stack>
# include <math.h>
# include <stdio.h>
# include <string.h>
# include <iostream>
# include <algorithm>
using namespace std;

int a[1000010];

int main(void)
{
    int n;
    while(~scanf("%d", &n) && n)
    {
        a[0] = 0, a[1] = 0, a[2] = 1;
        for(int i = 3; i <= n; i++)
            a[i] = i%2;
        int k = floor(sqrt(n)+0.5);
        for(int i = 3; i <= k; i++)
        {
            if(a[i])
            {
                for(int j = 2*i; j <= n; j += i)
                {
                    a[j] = 0;
                }
            }
        }
        int sum = 0;
        for(int i = 1; i <= n; i++)
        {
            if(a[i])
                sum++;
        }
        printf("%d\n", sum);
    }

    return 0;
}