莫比乌斯入门：bzoj 1101 Zap（Mobius）

传送门
题解：

#include<bits/stdc++.h>using namespace std;const int MAXN=50002,INF=0x3f3f3f3f;int mu[MAXN],prime[MAXN],tot=0;bool vis[MAXN];inline void linear_shaker() {    memset(vis,false,sizeof(vis));    mu[1]=1;    for (register int i=2;i<MAXN;++i) {        if (!vis[i]) prime[++tot]=i,mu[i]=-1;        for (int j=1;j<=tot&&i*prime[j]<MAXN;++j) {            vis[i*prime[j]]=true;            if (i%prime[j]==0) {mu[i*prime[j]]=0;break;}            mu[i*prime[j]]=-mu[i];        }    }    for (register int i=2;i<MAXN;++i) mu[i]+=mu[i-1];}int main() {    linear_shaker();    int kase;    scanf("%d",&kase);    while (kase--) {        int n,m,d;        scanf("%d%d%d",&n,&m,&d);        n/=d,m/=d;        int ans=0,last=0,t=min(n,m);        for (int i=1;i<=t;i=last+1) {            last=min(n/(n/i),m/(m/i));            ans+=(mu[last]-mu[i-1])*(n/i)*(m/i);        }        printf("%d\n",ans);    }    return 0;}