银联高校极客挑战赛 B-整数对(莫比乌斯反演)

整数对

#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=1e5+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_64(ll x,ll y,ll c){return (x*y-(ll)((long double)x/c*y)*c+c)%c;}
inline ll ksm(ll a,ll b,ll c){ll ans=1;for(;b;b>>=1,a=a*a%c)if(b&1)ans=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 prime[N],tot=0;
short int mu[N];
bool vis[N];
void pre(){
    mu[1]=1;
    for(int i=2;i<N;i++){
        if(!vis[i])prime[++tot]=i,mu[i]=-1;
        for(int x=1;x<=tot&&i*prime[x]<N;x++){
            vis[i*prime[x]]=1;
            if(i%prime[x]==0){
                mu[i*prime[x]]=0;
                break;
            }else mu[i*prime[x]]=-mu[i];
        }
    }
}
int main(){
    pre();
    int t;cin>>t;
    while(t--){
        ll n,m,p;
        sc("%lld%lld%lld",&n,&m,&p);
        vector<int>d;
        for(int i=1;i*i<=p;i++){
            if(p%i==0){
                d.push_back(i);
                if(i!=p/i)d.push_back(p/i);
            }
        }
        int sz=d.size();
        int pn[N],pm[N];
        for(int i=0;i<sz;i++){
            int pi=p/d[i];
            ll res=0,ans=0;
            for(int x=1;x*x<=pi;x++){
                if(pi%x==0){
                    res+=mu[x]*(n/(d[i]*x));
                    ans+=mu[x]*(m/(d[i]*x));
                    if(x!=pi/x){
                        res+=mu[pi/x]*(n/(d[i]*(pi/x)));
                        ans+=mu[pi/x]*(m/(d[i]*(pi/x)));
                    }
                }
            }
            pn[pi]=res,pm[pi]=ans;
        }
        ll ans=0;
        for(int i=0;i<sz;i++){
            ll x=0;
            for(int j=0;j<sz;j++){
                if(1LL*d[i]*d[j]%p==0)x+=pm[p/d[j]];
            }
            ans+=x*pn[p/d[i]];
        }
        printf("%lld\n",ans);
    }       
}

#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=1e5+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_64(ll x,ll y,ll c){return (x*y-(ll)((long double)x/c*y)*c+c)%c;}
inline ll ksm(ll a,ll b,ll c){ll ans=1;for(;b;b>>=1,a=a*a%c)if(b&1)ans=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 prime[N],tot=0;
short int mu[N];
bool vis[N];
void pre(){
    mu[1]=1;
    for(int i=2;i<N;i++){
        if(!vis[i])prime[++tot]=i,mu[i]=-1;
        for(int x=1;x<=tot&&i*prime[x]<N;x++){
            vis[i*prime[x]]=1;
            if(i%prime[x]==0){
                mu[i*prime[x]]=0;
                break;
            }else mu[i*prime[x]]=-mu[i];
        }
    }
}
int main(){
    pre();
    int t;cin>>t;
    while(t--){
        ll n,m,p;
        sc("%lld%lld%lld",&n,&m,&p);
        vector<int>d;
        for(int i=1;i*i<=p;i++){
            if(p%i==0){
                d.push_back(i);
                if(i!=p/i)d.push_back(p/i);
            }
        }
        int sz=d.size();
        ll ans=0;
        for(int i=0;i<sz;i++){
            ll res=0;
            for(int j=1;j*j<=d[i];j++){
                if(d[i]%j==0){
                    res+=m/(p/j)*mu[d[i]/j];
                    if(j!=d[i]/j)res+=m/(p/(d[i]/j))*mu[d[i]/(d[i]/j)];
                }
            }
            ans+=res*(n/d[i]);
        }
        printf("%lld\n",ans);
    }
}