欧拉函数和欧拉定理

873. 欧拉函数 - AcWing题库

#include 
using namespace std;

int main() {
	int n;
	cin >> n;
	while (n--) {
		int a;
		cin >> a;
		int ret = a;
		for (int i = 2; i <= a / i; i++) {
			if (a % i == 0) {                        
				ret -= ret / i;
				while (a % i == 0) a /= i;
			}
		}   
		if (a > 1) ret -= ret / a;
		cout << ret << endl;
	}
	return 0;
}

 874. 筛法求欧拉函数 - AcWing题库

#include 
#include 
using namespace std;

const int N = 1e6 + 10;
int p[N] = { 0 };
vector v, st(N);
int main() {
	p[1] = 1;
	int n;
	cin >> n;
	for (int i = 2; i <= n; i++) {
		if (!st[i]) {
			v.push_back(i);
			p[i] = i - 1;
		}
		for (int j = 0; v[j] <= n / i; j++) {
			st[v[j] * i] = 1;
			if (i % v[j] == 0) {
				p[v[j] * i] = v[j] * p[i];
				break;
			}
			p[v[j] * i] = p[i] * (v[j] - 1);
		}
	}
	long long ans = 0;
	for (int i = 1; i <= n; i++) {
		ans += p[i];
	}
	cout << ans;
	return 0;
}

 欧拉定理： 

证明： 【欧拉定理】简单证明_哔哩哔哩_bilibili