选出来的个数能凑成或者必然有一个性质,。
$$
#include <bits/stdc++.h> using namespace std; typedef unsigned long long ull; typedef long long ll; const int N = 2e7 + 10; int prime[N], cnt; ull mu[N]; 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++) { mu[i] += mu[i - 1]; } } map<ll, ull> mp; ull Djs_mu(ll n) { if (n < N) { return mu[n]; } if (mp.count(n)) { return mp[n]; } ull ans = 1; for (ll l = 2, r; l <= n; l = r + 1) { r = n / (n / l); ans -= (r - l + 1) * Djs_mu(n / l); } return mp[n] = ans; } ull quick_pow(ull a, ll n) { ull ans = 1; while (n) { if (n & 1) { ans = ans * a; } a = a * a; n >>= 1; } 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(); ull n, m, ans = 0; cin >> n >> m; for (ull l = 1, r; l <= m; l = r + 1) { r = m / (m / l); ans += quick_pow(m / l, n) * (Djs_mu(r) - Djs_mu(l - 1)); } cout << ans << "\n"; return 0; }