UESTC 618 无平方因子数 ( 莫比乌斯)

UESTC 618 

题意：求1到n中无平方因子数的个数

 

Sample Input

3 
1 
10 
30

Sample Output

1 
7 
19

 

 

思路：与前面的BZOJ 2440相似

 

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <queue>
#include <vector>
#include <algorithm>
#include <functional>
typedef long long ll;
using namespace std;

const int inf = 0x3f3f3f3f;
const int maxn = 1e6+10;
int tot;
int is_prime[maxn];
int mu[maxn];
int prime[maxn];

void Moblus()
{
    tot = 0;
    mu[1] = 1;
    for(int i = 2; i < maxn; i++)
    {
        if(!is_prime[i])
        {
            prime[tot++] = i;
            mu[i] = -1;
        }

        for(int j = 0; j < tot && i*prime[j] < maxn; j++)
        {
            is_prime[i*prime[j]] = 1;
            if(i % prime[j])
            {
                mu[i*prime[j]] = -mu[i];
            }
            else
            {
                mu[i*prime[j]] = 0;
                break;
            }
        }
    }
}


int main()
{
    Moblus();
    int T;
    ll n;
    scanf("%d",&T);
    while(T--)
    {
        ll ans = 0;
        scanf("%lld",&n);
        for(ll i = 1;i*i <= n;i++)
            ans += (ll)mu[i]*(n/(i*i));
        printf("%lld\n",ans);
    }
}