[莫比乌斯反演] BZOJ 2820 YY的GCD

#include<cstdio>#include<cstdlib>#include<cstring>#include<algorithm>#include<cmath>using namespace std;typedef long long ll;inline char nc(){static char buf[100000],*p1=buf,*p2=buf;if (p1==p2) { p2=(p1=buf)+fread(buf,1,100000,stdin); if (p1==p2) return EOF; }return *p1++;}inline void read(int &x){char c=nc(),b=1;for (;!(c>='0' && c<='9');c=nc()) if (c=='-') b=-1;for (x=0;c>='0' && c<='9';x=x*10+c-'0',c=nc()); x*=b;}inline int write(ll x,char c){if (x==0) return putchar('0'),putchar(c),0;if (x<0) putchar('-'),x=-x;char s[50]={0},len=0;while (x) s[++len]=x%10+'0',x/=10;for (int i=len;i;i--) putchar(s[i]); putchar(c);}const int maxn=10000000;int mobius[maxn+5],sum[maxn+5];int vst[maxn+5],prime[maxn+5],num=0;ll f[maxn+5];inline void Pre(){mobius[1]=1;for (int i=2;i<=maxn;i++){if (!vst[i])mobius[i]=-1,prime[++num]=i;for (int j=1;j<=num && prime[j]*i<=maxn;j++){vst[i*prime[j]]=1;if (i%prime[j]==0){mobius[i*prime[j]]=0; break;}elsemobius[i*prime[j]]=-mobius[i];}}for (int i=1;i<=num;i++)for (int j=1;j*prime[i]<=maxn;j++)f[j*prime[i]]+=mobius[j];for (int i=1;i<=maxn;i++)f[i]+=f[i-1];}int n,m;ll ans;int main(){int Q;Pre();read(Q);while (Q--){read(n); read(m);if (n>m) swap(n,m);ans=0;for (int j,i=1;i<=n;i=j+1){j=min(n/(n/i),m/(m/i));ans+=(f[j]-f[i-1])*(n/i)*(m/i);}write(ans,'\n');}return 0;}