// #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 = 5e7 + 10; bool flag[N]; int minp[N]; vector prime; void prime_gen(int n = N) { fill(flag, flag + n, false); for (int i = 2; i < n; ++i) { if (!flag[i]) { prime.push_back(i); minp[i] = i; } for (int j = 0, k; j < SZ(prime) && (k = prime[j] * i) < n; ++j) { flag[k] = true; if (i % prime[j]) { minp[k] = prime[j]; } else { minp[k] = minp[i]; break; } } } trace(SZ(prime)); } int main() { int n; cin >> n; prime_gen(n + 1); vector dp(n + 1); for (int i = 1, ni, k = 1; i <= n; i = ni, ++k) { ni = min(i + k * 2 + 1, n + 1); for (int j = i; j < ni; ++j) dp[j] = k; } vector f(n + 1); f[1] = 1; int64 ret = dp[n]; for (int k = 2; k <= n; ++k) { // if (k % 1000000 == 0) trace(k); int p = minp[k]; f[k] = f[k / p]; if (f[k] % p == 0) { f[k] /= p; } else { f[k] *= p; } ret += dp[n / f[k]]; } cout << ret << '\n'; return 0; }