[SDOI2012] Longge 的问题

题意

求$\sum _i^{n}gcd(i,n)$

想法

套路题
$\sum _i^{n}gcd(i,n)$ $=$ $\sum _{i,i|n}i\ast phi（n/i）$
枚举$i$暴力求$phi$

代码

#include<iostream>
#include<cstdio>
#include<cmath>
#define ll long long

ll n;

ll phi(ll now){
	ll ans = now;
	for(ll i = 2;i * i <= now;++i){
		if(now % i == 0){
			ans = ans / i * (i - 1);
			while(now % i == 0) now /= i;
		}
	}
	if(now > 1) ans = ans / now * (now - 1);
	return ans;
}

ll ans = 0;

int main(){
	scanf("%lld",&n);
	ll s = sqrt(n);
	for(ll i = 1;i <= s;++i){
		if(n % i == 0){
			ans += phi(n / i) * i;
			if(i * i != n)
			ans += phi(i) * (n / i);
		}
	}
	std::cout<<ans<<std::endl;
}