BZOJ-4804 欧拉心算(莫比乌斯反演)

BZOJ-4804 欧拉心算

1. 莫比乌斯反演
   
2. 欧拉函数
   

#include<bits/stdc++.h>
#define me(a,x) memset(a,x,sizeof(a))
#define IN freopen("in.txt","r",stdin);
#define OUT freopen("out.txt","w",stdout);
#define sc scanf
#define itn int
#define STR clock_t startTime = clock();
#define END clock_t endTime = clock();cout << double(endTime - startTime) / CLOCKS_PER_SEC *1000<< "ms" << endl;
using namespace std;
const int N=1e7+5;
const long long mod=1e9+7;
const long long mod2=998244353;
const int oo=0x7fffffff;
const int sup=0x80000000;
typedef long long ll;
typedef unsigned long long ull;
template <typename it>void db(it *begin,it *end){while(begin!=end)cout<<(*begin++)<<" ";puts("");}
template <typename it>
string to_str(it n){string s="";while(n)s+=n%10+'0',n/=10;reverse(s.begin(),s.end());return s;}
template <typename it>int o(it a){cout<<a<<endl;return 0;}
inline ll mul(ll a,ll b,ll c){ll ans=0;for(;b;b>>=1,a=(a+a)%c)if(b&1)ans=(ans+a)%c;return ans;}
inline ll ksm(ll a,ll b,ll c){ll ans=1;for(;b;b>>=1,a=mul(a,a,c))if(b&1)ans=mul(ans,a,c);return ans;}
inline void exgcd(ll a,ll b,ll &x,ll &y){if(!b)x=1,y=0;else exgcd(b,a%b,y,x),y-=x*(a/b);}
int phi[N];
ll sum[N];
int prime[N],tot=0;
bool f[N]={0};
void pre(){
    phi[1]=1;
    for(int i=2;i<N;i++){
        if(!f[i])prime[++tot]=i,phi[i]=i-1;
        for(int j=1;j<=tot&&i*prime[j]<N;j++){
            f[i*prime[j]]=1;
            if(i%prime[j]==0){
                phi[i*prime[j]]=phi[i]*prime[j];
                break;
            }else{
                phi[i*prime[j]]=phi[i]*(prime[j]-1);
            }
        }
    }
    sum[0]=0;
    for(int i=1;i<N;i++){
        sum[i]=sum[i-1]+phi[i];
    }
}
int main(){
    int t;sc("%d",&t);
    pre();
    while(t--){
        int n;sc("%d",&n);
        ll ans=0;
        for(int d=1;d<=n;){
            int last=n/(n/d);
            ans+=(sum[last]-sum[d-1])*(2LL*sum[n/d]-1);
            d=last+1;
        }
        printf("%lld\n",ans);
    }
    return 0;
}