UVa 11426 GCD - Extreme (II) / 素数筛选 + 欧拉函数

输入正整数n,求gcd(1,2)+gcd(1,3)+gcd(2,3)+...+gcd(n-1,n)

设f(n) = gcd(1,n)+gcd(2,n)+...+gcd(n-1,n)

所求s(n) = f(2)+f(3)+...+f(n) = s(n-1)+f(n);

gcd(x,n) = i <=> gcd(x/i,n/i) = 1 满足条件的x/i有phi(n/i)个（欧拉函数）

可以按照素数筛选发那样做枚举因子i 然后f
+= i*phi[n/i];

phi_table 用到了素数筛选发求出从1到n的欧拉函数只 存在phi
中

#include <cstdio>
#include <cstring>
const int maxn = 4000010;
typedef long long LL;

LL s[maxn], f[maxn], phi[maxn+10];

void phi_table(int n)
{
	for(int i = 2; i <= n; i++)
		phi[i] = 0;
	phi[1] = 1;
	for(int i = 2; i <= n; i++)
	{
		if(!phi[i])
		{
			for(int j = i; j <= n; j += i)
			{
				if(!phi[j])
					phi[j] = j;
				phi[j] = phi[j] / i * (i-1);
			}
		}
	}
}

int main()
{
	phi_table(maxn);
	memset(f, 0, sizeof(f));
	for(int i = 1; i <= maxn; i++)
		for(int n = i*2; n <= maxn; n += i)
			f
 += i * phi[n / i];
	s[2] = f[2];
	for(int n = 3; n <= maxn; n++)
		s
 = s[n-1] + f
;
	int n;
	while(scanf("%d", &n), n)
		printf("%lld\n",s
);
	return 0;
}