P3327 [SDOI2015]约数个数和

 

 

 

 

#include <iostream>
#include <cstdio>
#include <queue>
#include <algorithm>
#include <cmath>
#include <cstring>
#define inf 2147483647
#define N 1000010
#define mod 1000000007
#define p(a) putchar(a)
#define For(i,a,b) for(int i=a;i<=b;++i)
//by war
//2020.8.7
using namespace std;
long long T,n,m,cnt,ans,a,b,c,d,k;
long long prime[N],mu[N],s[N];
bool vis[N];
void in(long long &x){
    long long y=1;char c=getchar();x=0;
    while(c<'0'||c>'9'){if(c=='-')y=-1;c=getchar();}
    while(c<='9'&&c>='0'){ x=(x<<1)+(x<<3)+c-'0';c=getchar();}
    x*=y;
}
void o(long long x){
    if(x<0){p('-');x=-x;}
    if(x>9)o(x/10);
    p(x%10+'0');
}

void Euler(int n){
    mu[1]=1;
    For(i,2,n){
        if(!vis[i]) prime[++cnt]=i,mu[i]=-1;
        for(int j=1;j<=cnt&&i*prime[j]<=n;j++){
            vis[i*prime[j]]=1;
            if(i%prime[j]==0){
                mu[i*prime[j]]=0;
                break;
            }
            mu[i*prime[j]]=-mu[i];
        }
    }
    For(i,1,n) mu[i]+=mu[i-1];
    For(x,1,n){
        for(int i=1,j;i<=x;i=j+1){
            j=x/(x/i);
            s[x]+=(j-i+1)*(x/i);
        }
    }
}

long long solve(long long n,long long m){
    long long r=0;
    for(int i=1,j;i<=n;i=j+1){
        j=min(n/(n/i),m/(m/i));
        r+=(mu[j]-mu[i-1])*s[n/i]*s[m/i];
    }
    return r;
}

signed main(){
    Euler(50000);
    in(T);
    while(T--){
        in(n);in(m);
        if(n>m) swap(n,m);
        ans=solve(n,m);
        o(ans);p('\n');
    }
    return 0;
}