Codeforces1036F Relatively Prime Powers 【容斥原理】

 1 #include<bits/stdc++.h>
 2 using namespace std;
 3 
 4 const long long LMAX = 9223372036854775807;
 5 
 6 long long n;
 7 int mu[100];
 8 
 9 void init(){
10     for(int i=2;i<=70;i++){
11     int p = i;
12     mu[i] = -1;
13     for(int j=2;j*j<=p;j++){
14         int cnt = 0; while(p%j == 0) p/=j,cnt++;
15         if(cnt != 1 && cnt != 0) mu[i] = 0;
16         else if(cnt == 1) mu[i]*=-1;
17     }
18     if(p != 1) mu[i]*=-1;
19     }
20 }
21 
22 long long fast_pow(int now,int pw){
23     long long ans = 1,dt = now;
24     int bit = 1;
25     while(bit <= pw){
26     if(bit & pw){
27         if(ans < LMAX/dt) ans *= dt;
28         else ans = LMAX;
29     }
30     if(dt < LMAX/dt) dt *= dt;
31     else dt = LMAX;
32     bit<<=1;
33     }
34     return ans;
35 }
36 
37 void work(){
38     long long ans = 0;
39     for(int i=2;i<=70;i++){
40     if(mu[i] == 0) continue;
41     int z = pow((long double)n,1.0/(long double)i);
42     if(z == 1) break;
43     if(fast_pow(z,i) > n) z--;
44     if(fast_pow(z+1,i) <= n) z++;
45     z--; ans += z*mu[i];
46     }
47     n -= ans;n--;
48     printf("%I64d\n",n);
49 }
50 
51 int main(){
52     int Tmp; scanf("%d",&Tmp);
53     init();
54     while(Tmp--){
55     scanf("%I64d",&n);
56     work();
57     }
58     return 0;
59 }