正题

题目链接:https://www.luogu.org/problemnew/show/P2568

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题目大意

求有多少个数对满足$gcd(x,y)=pri(x,y\le n)$

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解题思路

首先对于
$$gcd(x,y)=p$$
$$=>gcd(x/p,y/p)=1$$
那么对数就是$$(\sum _{i=1}^n\phi (i))\ast 2-1$$
枚举就好了

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$code$

#include<cstdio>
#include<algorithm>
#define ll long long
using namespace std;
const ll N=1e7+100;
ll n,phi[N],pri[N],tot,ans;
int main()
{scanf("%lld",&n);phi[1]=1;for(ll i=2;i<=n;i++)if(!phi[i]){pri[++tot]=i;for(ll j=i;j<=n;j+=i){if(!phi[j]) phi[j]=j;phi[j]=phi[j]/i*(i-1);}}for(ll i=1;i<=n;i++)phi[i]+=phi[i-1];for(ll i=1;i<=tot;i++)ans+=phi[n/pri[i]]*2-1;printf("%lld",ans);
}