[bzoj3994]约数个数和

#include<bits/stdc++.h>
using namespace std;
#define N 50005
long long n,m,ans,mu[N],f[N],t[N],vis[N],p[N];
void xxs(int n){
    mu[1]=f[1]=1;
    for(int i=2;i<=n;i++){
        if (!vis[i]){
            p[++p[0]]=i;
            mu[i]=-1;
            t[i]=1;
            f[i]=2;
        }
        for(int j=1;(j<=p[0])&&(i*p[j]<=n);j++){
            vis[i*p[j]]=1;
            if (i%p[j]==0){
                t[i*p[j]]=t[i]+1;
                f[i*p[j]]=f[i]/(t[i]+1)*(t[i]+2);
                break;
            }
            t[i*p[j]]=1;
            f[i*p[j]]=f[i]*2;
            mu[i*p[j]]=-mu[i];
        }
    }
    for(int i=2;i<=n;i++){
        f[i]+=f[i-1];
        mu[i]+=mu[i-1];
    }
}
int main(){
    xxs(N-5);
    int t;
    scanf("%d",&t);
    while (t--){
        scanf("%lld%lld",&n,&m);
        if (n>m)swap(n,m);
        ans=0;
        for(int i=1,j;i<=n;i=j+1){
            j=min(n/(n/i),m/(m/i));
            ans+=(mu[j]-mu[i-1])*f[n/i]*f[m/i];
        }
        printf("%lld\n",ans);
    }
}