[POI2007]ZAP-Queries [莫比乌斯反演]

​​传送门​​

对于本题 (一下来源于luogu题解)

 

 然后求一个mu的前缀和 , 整除分块搞一下

---

#include<bits/stdc++.h>
#define N 50051
#define LL long long
using namespace std;
int mu[N],prim[N],isp[N],s[N],T,tot;
void Init(){
  mu[1] = s[1] = 1;
  for(int i=2;i<=N-50;i++){
    if(!isp[i]){
      prim[++tot]=i;
      mu[i] = -1;
    }
    for(int j=1;j<=tot;j++){
      if(prim[j]*i >= N-50) break;
      isp[prim[j]*i] = 1;
      mu[prim[j]*i] = -mu[i];
      if(i%prim[j]==0){
        mu[prim[j]*i]=0; 
        break;
      }
    }
    s[i] = s[i-1] + mu[i];
  }
}
void Solve(){
  int n,m,d; scanf("%d%d%d",&n,&m,&d);
  if(n>m) swap(n,m); n/=d; m/=d;
  LL ans = 0;
  for(int l=1,r;l<=n;l=r+1){
    int x1 = n/l , x2 = m/l;
    r = min(n/x1,m/x2);
    ans += (LL)(s[r] - s[l-1]) * x1 * x2;
  }printf("%lld\n",ans);
}
int main(){
  scanf("%d",&T); Init();
  while(T--) Solve(); return 0;
}