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bzoj2818Gcd

若如初梘 2022-08-08 阅读 27


Description
给定整数N,求1<=x,y<=N且Gcd(x,y)为素数的
数对(x,y)有多少对.

Input
一个整数N

Output
如题

Sample Input
4

Sample Output
4
HINT
hint

对于样例(2,2),(2,4),(3,3),(4,2)

1<=N<=10^7

bzoj2818Gcd_#define

#include<cstdio>
#include<algorithm>
#define N 10001000
#define rg register
#define ll long long
using namespace std;
int n,mu[N],prime[N/10],tot,s[N];ll ans;
bool not_prime[N];
int main(){
// freopen("bzoj2818.in","r",stdin);
scanf("%d",&n);mu[1]=1;
for (rg int i=2;i<=n;++i){
if (!not_prime[i]) prime[++tot]=i,mu[i]=-1;
for (int j=1;prime[j]*i<=n;++j){
not_prime[i*prime[j]]=1;
if (i%prime[j]==0){
mu[i*prime[j]]=0;break;
}else mu[i*prime[j]]=-mu[i];
}
}
for (rg int i=1;i<=tot;++i){
const int p=prime[i];
for (rg int i=1;p*i<=n;++i) s[p*i]+=mu[i];
}int last=1;
for (rg int i=1;i<=n;++i) s[i]+=s[i-1];
for (rg int i=1;i<=n;i=last+1){
last=n/(n/i);ans+=(ll)(n/i)*(n/i)*(s[last]-s[i-1]);
}printf("%lld\n",ans);
return 0;
}


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