洛谷P2257 YY的GCD

莫比乌斯反演

还是把gcd换成莫比乌斯函数，在最外层枚举素数p，对于每个素数p，gcd莫比乌斯反演

#include <bits/stdc++.h>
#define INF 0x3f3f3f3f
#define full(a, b) memset(a, b, sizeof a)
#define FAST_IO ios::sync_with_stdio(false), cin.tie(0), cout.tie(0)
using namespace std;
typedef long long ll;
inline int lowbit(int x){ return x & (-x); }
inline int read(){
    int X = 0, w = 0; char ch = 0;
    while(!isdigit(ch)) { w |= ch == '-'; ch = getchar(); }
    while(isdigit(ch)) X = (X << 3) + (X << 1) + (ch ^ 48), ch = getchar();
    return w ? -X : X;
}
inline int gcd(int a, int b){ return b ? gcd(b, a % b) : a; }
inline int lcm(int a, int b){ return a / gcd(a, b) * b; }
template<typename T>
inline T max(T x, T y, T z){ return max(max(x, y), z); }
template<typename T>
inline T min(T x, T y, T z){ return min(min(x, y), z); }
template<typename A, typename B, typename C>
inline A fpow(A x, B p, C lyd){
    A ans = 1;
    for(; p; p >>= 1, x = 1LL * x * x % lyd)if(p & 1)ans = 1LL * x * ans % lyd;
    return ans;
}
const int N = 10000005;
int _, n, m, tot, mo[N], prime[N], f[N];
bool vis[N];
ll sum[N];
void mobius(){
    mo[1] = 1;
    for(int i = 2; i < N; i ++){
        if(!vis[i]) prime[++tot] = i, mo[i] = -1;
        for(int j = 1; j <= tot && i * prime[j] < N; j ++){
            vis[i * prime[j]] = true;
            if(i % prime[j] == 0){
                mo[i * prime[j]] = 0;
                break;
            }
            else mo[i * prime[j]] = -mo[i];
        }
    }
    for(int i = 1; i <= tot; i ++){
        for(int j = 1; j * prime[i] < N; j ++) f[j * prime[i]] += mo[j];
    }
    for(int i = 2; i < N; i ++) sum[i] = sum[i - 1] + 1LL * f[i];
}

int main(){

    mobius();
    for(_ = read(); _; _ --){
        n = read(), m = read();
        ll ans = 0;
        for(int l = 1, r; l <= min(n, m); l = r + 1){
            r = min(n / (n / l), m / (m / l));
            ans += 1LL * (n / l) * (m / l) * (sum[r] - sum[l - 1]);
        }
        printf("%lld
", ans);
    }
    return 0;
}