#define LOCAL #define _USE_MATH_DEFINES #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; template ostream& operator <<(ostream& out, const pair& a) { out << "(" << a.first << "," << a.second << ")"; return out; } template ostream& operator <<(ostream& out, const array& a) { out << "["; bool first = true; for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "]"; return out; } template ostream& operator <<(ostream& out, const vector& a) { out << "["; bool first = true; for (auto v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "]"; return out; } template ostream& operator <<(ostream& out, const set& a) { out << "{"; bool first = true; for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "}"; return out; } template ostream& operator <<(ostream& out, const map& a) { out << "{"; bool first = true; for (auto& p : a) { out << (first ? "" : ", "); out << p.first << ":" << p.second; first = 0;} out << "}"; return out; } #ifdef LOCAL #define trace(...) __f(#__VA_ARGS__, __VA_ARGS__) #else #define trace(...) 42 #endif template void __f(const char* name, Arg1&& arg1){ cerr << name << ": " << arg1 << endl; } template void __f(const char* names, Arg1&& arg1, Args&&... args){ const char* comma = strchr(names + 1, ','); cerr.write(names, comma - names) << ": " << arg1 << " |"; __f(comma + 1, args...); } template auto vect(const T& v, int n) { return vector(n, v); } template auto vect(const T& v, int n, D... m) { return vector(n, vect(v, m...)); } typedef long long int64; typedef pair ii; #define SZ(x) (int)((x).size()) template static constexpr T inf = numeric_limits::max() / 2; const int MOD = 1e9 + 7; // const int MOD = 998244353; mt19937 mrand(random_device{}()); int rnd(int x) { return mrand() % x; } // mt19937_64 mrand(random_device{}()); // int64 rnd(int64 x) { return mrand() % x; } template void out(const vector& a) { for (int i = 0; i < SZ(a); ++i) cout << a[i] << " \n"[i + 1 == SZ(a)]; } template bool ckmin(T& a, const T& b) { return b < a ? a = b, 1 : 0; } template bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; } template void dedup(vector& v) { sort(v.begin(), v.end()); v.erase(unique(v.begin(), v.end()), v.end()); } void add(int& x, int y) { x += y; if (x >= MOD) x -= MOD; } struct fast_ios { fast_ios() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(10); }; } fast_ios_; const int N = 100; bool flag[N]; int mu[N]; vector prime; void mu_gen(int n = N) { fill(flag, flag + n, false); mu[1] = 1; for (int i = 2; i < n; ++i) { if (!flag[i]) { prime.push_back(i); mu[i] = -1; } for (int j = 0, k; j < SZ(prime) && (k = prime[j] * i) < n; ++j) { flag[k] = true; if (i % prime[j]) { mu[k] = -mu[i]; } else { mu[k] = 0; break; } } } } __int128 power(int64 x, int64 n) { __int128 ret = 1; for (int i = 0; i < n; ++i) ret *= x; return ret; } int64 solve(int64 n) { int64 ret = 1; for (int k = 2; k <= 60; ++k) { int64 x = (int64)pow(1.0 * n, 1.0 / k); while (power(x + 1, k) <= n) ++x; while (power(x, k) > n) --x; ret -= (x - 1) * mu[k]; } return ret; } int main() { mu_gen(); // for (int i = 2; i < N; ++i) { // trace(i, mu[i]); // } int cas; cin >> cas; while (cas--) { int m; cin >> m; int64 low = 1, high = 1LL << 60; while (low != high) { int64 mid = (low + high) / 2; // trace(mid, solve(mid)); if (solve(mid) < m) { low = mid + 1; } else { high = mid; } } cout << high << '\n'; } return 0; }