莫比乌斯函数打表模板

• 莫比乌斯打表（phi可以删除）
• phi–欧拉函数表 miu–莫比乌斯函数表 fac–i最大的素因子辅助打phi表

int phi[maxn],miu[maxn],fac[maxn];
ll f[maxn], F[maxn];
void init()
{
	for (int i = 1; i < maxn; ++i) fac[i] = i;
	phi[1] = miu[1] = 1;
	for (int i = 2; i < maxn; ++i)
	{
		if (fac[i] == i)
			for (int j = i << 1; j < maxn; j += i)
				fac[j] = i; 
		if (i / fac[i] % fac[i]) phi[i] = (fac[i] - 1)*phi[i / fac[i]], miu[i] = -miu[i / fac[i]]; //如果b质数  a%b！=0  phi(a*b) = phi(a)*b - phi(a)
		else phi[i] = fac[i] * phi[i / fac[i]], miu[i] = 0;										//当b是质数，a%b==0，phi(a*b)=phi(a)*b 
	}
}

• 求一个数的欧拉函数值–复杂度n^1/2

int miu(ll n){
	int prime = 1;
	int flag = 0;
	for (int i = 2; i*i <= n; i++) {
		if (n%i == 0) {
			prime++;
			n /= i;
			if (n%i == 0) {
				flag = 1;
				break;
			}
		}
	}
	if (flag) 
		return 0;
	if (prime % 2)return -1;
	else return 1;
}