最大公约数和

题面

所以给定一个整数N，你需要求出∑gcd(i, N)(1<=i <=N)
N<=MAXINT

Sol

式子就是(sum_{d|N}d*phi(N/d))
没了

# include <bits/stdc++.h>
# define RG register
# define IL inline
# define Fill(a, b) memset(a, b, sizeof(a))
using namespace std;
typedef long long ll;
const int _(1e7 + 1);

IL ll Read(){
    char c = '%'; ll x = 0, z = 1;
    for(; c > '9' || c < '0'; c = getchar()) if(c == '-') z = -1;
    for(; c >= '0' && c <= '9'; c = getchar()) x = x * 10 + c - '0';
    return x * z;
}

IL ll Phi(RG ll x){
	RG ll cnt = x;
	for(RG ll i = 2; i <= x; ++i){
		if(x % i) continue;
		while(x % i == 0) x /= i;
		cnt -= cnt / i;
	}
	if(x > 1) cnt -= cnt / x;
	return cnt;
}

int main(RG int argc, RG char *argv[]){
	RG ll n = Read(), ans = 0, m = sqrt(n);
	for(RG ll i = 1; i <= m; ++i){
		if(n % i) continue;
		ans += 1LL * i * Phi(n / i);
		if(i * i != n) ans += 1LL * (n / i) * Phi(i);
	}
	printf("%lld
", ans);
	return 0;
}