HRY and mobius

HRY and mobius

• 对于k = 0 ，显然最后答案为，n。

• 对于k = 1，答案就是这就是经典的杜教筛问题了。

• 对于k = 2
  

/*
  Author : lifehappy
*/
#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

const int N = 1e7 + 10;

int prime[N], mu[N], sum[N], cnt;

bool st[N];

void init() {
    mu[1] = 1;
    for(int i = 2; i < N; i++) {
        if(!st[i]) {
            prime[++cnt] = i;
            mu[i] = -1;
        }
        for(int j = 1; j <= cnt && 1ll * i * prime[j] < N; j++) {
            st[i * prime[j]] = 1;
            if(i % prime[j] == 0) {
                break;
            }
            mu[i * prime[j]] = -mu[i];
        }
    }
    for(int i = 1; i < N; i++) {
        sum[i] = mu[i] + sum[i - 1];
    }
}

unordered_map<ll, ll> ans_s;

ll Djs(ll n) {
    if(n < N) return sum[n];
    if(ans_s.count(n)) return ans_s[n];
    ll ans = 1;
    for(ll l = 2, r; l <= n; l = r + 1) {
        r = n / (n / l);
        ans -= (r - l + 1) * Djs(n / l);
    }
    return ans_s[n] = ans;
}

ll calc(ll n) {
    ll ans = 0;
    for(ll i = 1; i * i <= n; i++) {
        ans += mu[i] * (n / i / i);
    }
    return ans;
}

int main() {
    // freopen("in.txt", "r", stdin);
    // freopen("out.txt", "w", stdout);
    // ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
    init();
    int T;
    scanf("%d", &T);
    while(T--) {
        ll n, k;
        scanf("%lld %lld", &n, &k);
        if(k == 0) {
            printf("%lld\n", n);
        }
        else if(k & 1) {
            printf("%lld\n", Djs(n));
        }
        else {
            printf("%lld\n", calc(n));
        }
    }
    return 0;
}