[莫比乌斯反演] BZOJ1101: [POI2007]Zap

#include<cstdio>
#include<algorithm>
using namespace std;
const int maxn=50005;
typedef long long LL;
int n,N=50000,p[maxn],mu[maxn];
bool vis[maxn];
void get_mu(){
mu[1]=1;
for(int i=2;i<=N;i++){
if(!vis[i]) p[++p[0]]=i, mu[i]=-1;
for(int j=1;j<=p[0]&&(LL)i*p[j]<=N;j++){
vis[i*p[j]]=true;
if(i%p[j]==0){ mu[i*p[j]]=0; break; }
mu[i*p[j]]=-mu[i];
}
}
for(int i=1;i<=N;i++) mu[i]+=mu[i-1];
}
int _test;
LL ans;
int main(){
freopen("bzoj1101.in","r",stdin);
freopen("bzoj1101.out","w",stdout);
get_mu();
scanf("%d",&_test);
while(_test--){
int n,m,d; scanf("%d%d%d",&n,&m,&d);
ans=0;
n/=d; m/=d; int _min=min(n,m);
for(int i=1,nxt;i<=_min;i=nxt+1){
nxt=min(n/(n/i),m/(m/i));
ans+=(LL)(n/i)*(m/i)*(mu[nxt]-mu[i-1]);
}
printf("%lld\n",ans);
}
return 0;
}