Problem p02624 (C++) — buggy submission, verdict: Time Limit Exceeded

#include "bits/stdc++.h"
#include <random>
using namespace std;
using ll = long long;
using dd = double;
using pll = pair<ll, ll>;
using tll = tuple<ll, ll, ll>;
using vll = vector<ll>;
using vdd = vector<dd>;
using vpll = vector<pll>;
using vtll = vector<tll>;
using vvll = vector<vll>;
using vvdd = vector<vdd>;
using vvpll = vector<vpll>;
using vvtll = vector<vtll>;
using vvvll = vector<vvll>;
using vvvdd = vector<vvdd>;
using vvvpll = vector<vvpll>;
using vvvtll = vector<vvtll>;
using vvvvll = vector<vvvll>;
using vvvvdd = vector<vvvdd>;
using vvvvpll = vector<vvvpll>;
using vvvvtll = vector<vvvtll>;

constexpr ll INF = 1LL << 60;
constexpr dd EPS = 1e-11;
constexpr dd PI = 3.1415926535897932;

// cin,cout高速化のおまじない＋桁数指定
struct Fast {
  Fast() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(std::numeric_limits<double>::max_digits10);
  }
} fast;

#define REPS(i, S, E) for (ll i = (S); i <= (E); i++)
#define rep(i, S, E) for (ll i = (S); i <= (E); i++)
#define REP(i, N) REPS(i, 0, (N)-1)
#define DEPS(i, S, E) for (ll i = (E); i >= (S); i--)
#define dep(i, E, S) for (ll i = (E); i >= (S); i--)
#define DEP(i, N) DEPS(i, 0, (N)-1)
#define EACH(e, v) for (auto &&e : v)
#define each(e, v) for (auto &&e : v)
#define ALL(v) (v).begin(), (v).end()
#define RALL(v) (v).rbegin(), (v).rend()

template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline T MaxE(vector<T> &v, ll S, ll E) {
  T m = v[S];
  REPS(i, S, E) chmax(m, v[i]);
  return m;
} // v[S]～v[E]の最大値
template <class T> inline T MinE(vector<T> &v, ll S, ll E) {
  T m = v[S];
  REPS(i, S, E) chmin(m, v[i]);
  return m;
} // v[S]～v[E]の最小値
template <class T> inline T MaxE(vector<T> &v, ll N) {
  return MaxE(v, 0, N - 1);
} // 先頭N個中の最大値
template <class T> inline T MinE(vector<T> &v, ll N) {
  return MinE(v, 0, N - 1);
}
template <class T> inline T MaxE(vector<T> &v) { return MaxE(v, (ll)v.size()); }
template <class T> inline T MinE(vector<T> &v) { return MinE(v, (ll)v.size()); }
template <class T> inline ll MaxI(vector<T> &v, ll S, ll E) {
  ll m = S;
  REPS(i, S, E) {
    if (v[i] > v[m])
      m = i;
  }
  return m;
}
template <class T> inline ll MinI(vector<T> &v, ll S, ll E) {
  ll m = S;
  REPS(i, S, E) {
    if (v[i] < v[m])
      m = i;
  }
  return m;
}
template <class T> inline ll MaxI(vector<T> &v, ll N) {
  return MaxI(v, 0, N - 1);
}
template <class T> inline ll MinI(vector<T> &v, ll N) {
  return MinI(v, 0, N - 1);
}
template <class T> inline ll MaxI(vector<T> &v) {
  return MaxI(v, (ll)v.size());
}
template <class T> inline ll MinI(vector<T> &v) {
  return MinI(v, (ll)v.size());
}
template <class T> inline T Sum(vector<T> &v, ll S, ll E) {
  T s = v[S];
  REPS(i, S + 1, E) s += v[i];
  return s;
}
template <class T> inline T Sum(vector<T> &v, ll N) { return Sum(v, 0, N - 1); }
template <class T> inline T Sum(vector<T> &v) { return Sum(v, v.size()); }
template <class T> inline ll sz(T &v) { return (ll)v.size(); }
template <class T> inline T POW(T a, ll n) {
  T r = 1;
  for (; n > 0; n >>= 1, a *= a) {
    if (n & 1)
      r *= a;
  }
  return r;
}
inline ll POW(int a, ll n) { return POW((ll)a, n); }
inline ll CEIL(ll a, ll b) { return (a + b - 1) / b; }
ll Gcd(ll a, ll b) { return (b == 0) ? a : Gcd(b, a % b); }
ll Lcm(ll a, ll b) { return a * b / Gcd(a, b); }
inline ll MSB(ll a) {
  for (ll o = 63, x = -1;;) {
    ll m = (o + x) / 2;
    if (a < (1LL << m))
      o = m;
    else
      x = m;
    if (o - x == 1)
      return x;
  }
}
inline ll Upper2N(ll s) { return 1LL << MSB(s) << 1; } // s<2^nなる最小の2^n
inline vll Bit2Idx(ll m) {
  vll v;
  for (ll i = 0; m; m >>= 1, i++)
    if (m & 1)
      v.push_back(i);
  return move(v);
}
inline ll BitNum(ll m) {
  for (ll c = 0;; m >>= 1) {
    c += m & 1;
    if (!m)
      return c;
  }
}
inline ll Bit(ll s, ll i) { return (s >> i) & 1; } // sの第ibit i=0-63
[[nodiscard]] inline ll BitOn(ll s, ll i) {
  return s | (1LL << i);
} // sの第ibitON i=0-63
[[nodiscard]] inline ll BitOff(ll s, ll i) {
  return s & ~(1LL << i);
} // sの第ibitOFF i=0-63
[[nodiscard]] inline ll BitCut(ll s, ll i) {
  return s & (1LL << ++i) - 1;
} // sの第0～第ibitを抽出
inline vll str2num(string &s, ll N) {
  vll v(N);
  REP(i, N) v[i] = (ll)(s[i] - '0');
  return move(v);
}
inline vll ALP2num(string &s, ll N) {
  vll v(N);
  REP(i, N) v[i] = (ll)(s[i] - 'A');
  return move(v);
}
inline vll alp2num(string &s, ll N) {
  vll v(N);
  REP(i, N) v[i] = (ll)(s[i] - 'a');
  return move(v);
}
template <class T> inline ll FloorIdx(vector<T> &v, T x) {
  return upper_bound(ALL(v), x) - v.begin() - 1;
}
template <class T> inline ll CeilIdx(vector<T> &v, T x) {
  return lower_bound(ALL(v), x) - v.begin();
}
template <class T>
inline ll UnderNumOf(vector<T> &v, T x) { // sort済vのx以下の個数を得る
  return upper_bound(v.begin(), v.end(), x) - v.begin();
}
template <class T, class Pr>
inline ll UnderNumOf(vector<T> &v, T x, Pr pred) { // x以下個数
  return upper_bound(v.begin(), v.end(), x, pred) - v.begin();
}
template <class T>
inline ll OverNumOf(vector<T> &v, T x) { // sort済vのx以上の個数を得る
  return (ll)v.size() - (lower_bound(v.begin(), v.end(), x) - v.begin());
}
template <class T, class Pr>
inline ll OverNumOf(vector<T> &v, T x, Pr pred) { // x以上の個数
  return (ll)v.size() - (lower_bound(v.begin(), v.end(), x, pred) - v.begin());
}

template <class T = ll> inline vector<T> cinv(ll N) {
  vector<T> v(N);
  REP(i, N) cin >> v[i];
  return move(v);
}
template <class T = ll, class S = ll> inline vector<pair<T, S>> cinv2(ll N) {
  vector<pair<T, S>> v(N);
  REP(i, N) { cin >> v[i].first >> v[i].second; }
  return move(v);
}
template <class T = ll, class S = ll, class R = ll>
inline vector<tuple<T, S, R>> cinv3(ll N) {
  vector<tuple<T, S, R>> v(N);
  REP(i, N) { cin >> get<0>(v[i]) >> get<1>(v[i]) >> get<2>(v[i]); }
  return move(v);
}
template <class T = ll, class S = ll, class R = ll, class Q = ll>
inline vector<tuple<T, S, R, Q>> cinv4(ll N) {
  vector<tuple<T, S, R, Q>> v(N);
  REP(i, N) {
    cin >> get<0>(v[i]) >> get<1>(v[i]) >> get<2>(v[i]) >> get<3>(v[i]);
  }
  return move(v);
}
template <class T = ll> inline vector<vector<T>> cinvv(ll N, ll M) {
  vector<vector<T>> vv(N);
  REP(i, N) vv[i] = cinv(M);
  return move(vv);
}
template <class T> inline void coutv(vector<T> &v, string d = " ") {
  ll N = (ll)v.size();
  REP(i, N) { cout << v[i] << ((i == N - 1) ? "" : d); }
  cout << '\\n';
}
template <class T> inline void coutv(deque<T> &v, string d = " ") {
  ll N = (ll)v.size();
  REP(i, N) { cout << v[i] << ((i == N - 1) ? "" : d); }
  cout << '\\n';
}
template <class T> void bye(T a) {
  cout << a << '\\n';
  exit(0);
}

#if defined(_DEBUG)
ll dumpW = 5;
template <class T> void Dump(vector<T> &v) {
  REP(i, (ll)v.size()) {
    cerr << ((i == 0) ? "[" : " ") << setw(dumpW) << v[i];
  }
  cerr << "]";
}
void Dump(vll &v) {
  REP(i, (ll)v.size()) {
    cerr << ((i == 0) ? "[" : " ") << setw(dumpW);
    if (v[i] == INF)
      cerr << "INF";
    else if (v[i] == -INF)
      cerr << "-INF";
    else
      cerr << v[i];
  }
  cerr << "]";
}
template <class T> void Dump(vector<vector<T>> &v) {
  ll N = (ll)v.size();
  string d[2][2] = {{" ", "["}, {"\\n", "]\\n"}};
  REP(i, N) {
    cerr << d[0][i == 0];
    Dump(v[i]);
    cerr << d[1][i == N - 1];
  }
}
template <class T> void Dump(vector<vector<vector<T>>> &v) {
  ll N = (ll)v.size();
  string d[2] = {"  <", "[ <"};
  REP(i, N) {
    cerr << d[i == 0] << i << ">\\n";
    Dump(v[i]);
  }
  cerr << "]\\n";
}
template <class T> void Dump(vector<vector<vector<vector<T>>>> &v) {
  ll N = (ll)v.size();
  string d[2] = {"  ---<", "[ ---<"};
  REP(i, N) {
    cerr << d[i == 0] << i << ">---\\n";
    Dump(v[i]);
  }
  cerr << "]\\n";
}
template <class T> void Dump(vector<vector<vector<vector<vector<T>>>>> &v) {
  ll N = (ll)v.size();
  string d[2] = {"  ======<", "[ ======<"};
  REP(i, N) {
    cerr << d[i == 0] << i << ">======\\n";
    Dump(v[i]);
  }
  cerr << "]\\n";
}
#else
template <class T> void Dump(vector<T> &v) {}
template <class T> void Dump(vector<vector<T>> &v) {}
template <class T> void Dump(vector<vector<vector<T>>> &v) {}
template <class T> void Dump(vector<vector<vector<vector<T>>>> &v) {}
template <class T> void Dump(vector<vector<vector<vector<vector<T>>>>> &v) {}
#endif

template <ll MOD> struct mll_ {
  ll val;
  mll_(ll v = 0) : val(v % MOD) {
    if (val < 0)
      val += MOD;
  }
  mll_ operator-() const { return -val; }
  mll_ operator+(const mll_ &b) const { return val + b.val; }
  mll_ operator-(const mll_ &b) const { return val - b.val; }
  mll_ operator*(const mll_ &b) const { return val * b.val; }
  mll_ operator/(const mll_ &b) const { return mll_(*this) /= b; }
  mll_ operator+(ll b) const { return *this + mll_(b); }
  mll_ operator-(ll b) const { return *this - mll_(b); }
  mll_ operator*(ll b) const { return *this * mll_(b); }
  friend mll_ operator+(ll a, const mll_ &b) { return b + a; }
  friend mll_ operator-(ll a, const mll_ &b) { return -b + a; }
  friend mll_ operator*(ll a, const mll_ &b) { return b * a; }
  friend mll_ operator/(ll a, const mll_ &b) { return mll_(a) / b; }
  mll_ &operator+=(const mll_ &b) {
    val = (val + b.val) % MOD;
    return *this;
  }
  mll_ &operator-=(const mll_ &b) {
    val = (val + MOD - b.val) % MOD;
    return *this;
  }
  mll_ &operator*=(const mll_ &b) {
    val = (val * b.val) % MOD;
    return *this;
  }
  mll_ &operator/=(const mll_ &b) {
    ll c = b.val, d = MOD, u = 1, v = 0;
    while (d) {
      ll t = c / d;
      c -= t * d;
      swap(c, d);
      u -= t * v;
      swap(u, v);
    }
    val = val * u % MOD;
    if (val < 0)
      val += MOD;
    return *this;
  }
  mll_ &operator+=(ll b) { return *this += mll_(b); }
  mll_ &operator-=(ll b) { return *this -= mll_(b); }
  mll_ &operator*=(ll b) { return *this *= mll_(b); }
  mll_ &operator/=(ll b) { return *this /= mll_(b); }
  bool operator==(const mll_ &b) { return val == b.val; }
  bool operator!=(const mll_ &b) { return val != b.val; }
  bool operator==(ll b) { return *this == mll_(b); }
  bool operator!=(ll b) { return *this != mll_(b); }
  friend bool operator==(ll a, const mll_ &b) { return mll_(a) == b.val; }
  friend bool operator!=(ll a, const mll_ &b) { return mll_(a) != b.val; }
  friend ostream &operator<<(ostream &os, const mll_ &a) { return os << a.val; }
  friend istream &operator>>(istream &is, mll_ &a) { return is >> a.val; }
  static mll_ Combination(ll a, ll b) {
    chmin(b, a - b);
    if (b < 0)
      return mll_(0);
    mll_ c = 1;
    REP(i, b) c *= a - i;
    REP(i, b) c /= i + 1;
    return c;
  }
};
using mll = mll_<1000000007LL>; // 1000000007LL;// 998244353LL;
using vmll = std::vector<mll>;
using vvmll = std::vector<vmll>;
using vvvmll = std::vector<vvmll>;
using vvvvmll = std::vector<vvvmll>;
using vvvvvmll = std::vector<vvvvmll>;

pair<vll, vector<bool>> eratosthenes(ll n) {
  vll primes;
  vector<bool> table(n + 1);
  table[0] = table[1] = true;
  rep(i, 2, n) {
    if (table[i])
      continue;
    primes.push_back(i);
    for (ll j = 2; i * j <= n; j++)
      table[i * j] = true;
  }
  return move(make_pair(move(primes), move(table)));
}

void solve() {
  ll n;
  cin >> n;
  vll primes;
  vector<bool> ptable;
  tie(primes, ptable) = eratosthenes(n);
  ll m = sz(primes);

  vll f(n + 1);
  f[1] = 1;

  ll ans = 1;
  rep(k, 2, n) {
    if (!ptable[k]) { // 素数なら
      f[k] = 2;
      ans += k * f[k];
      continue;
    }

    ll val = k;
    rep(i, 0, m - 1) {
      ll p = primes[i];
      if (p * p > val)
        break;

      ll ee = 0;
      while (true) {
        if (val % p > 0)
          break;
        ee++;
        val /= p;
      }
      if (ee == 0)
        continue;

      f[k] = f[val] * (ee + 1);
      break;
    }
    ans += f[k] * k;
  }
  cout << ans << '\\n';
}

int main() {
#if 1
  solve();
#else
  ll t;
  cin >> t;
  rep(i, 0, t - 1) { solve(); }
#endif
  return 0;
}


Error: TLE

Fixed submission:

#include "bits/stdc++.h"
#include <random>
using namespace std;
using ll = long long;
using dd = double;
using pll = pair<ll, ll>;
using tll = tuple<ll, ll, ll>;
using vll = vector<ll>;
using vdd = vector<dd>;
using vpll = vector<pll>;
using vtll = vector<tll>;
using vvll = vector<vll>;
using vvdd = vector<vdd>;
using vvpll = vector<vpll>;
using vvtll = vector<vtll>;
using vvvll = vector<vvll>;
using vvvdd = vector<vvdd>;
using vvvpll = vector<vvpll>;
using vvvtll = vector<vvtll>;
using vvvvll = vector<vvvll>;
using vvvvdd = vector<vvvdd>;
using vvvvpll = vector<vvvpll>;
using vvvvtll = vector<vvvtll>;

constexpr ll INF = 1LL << 60;
constexpr dd EPS = 1e-11;
constexpr dd PI = 3.1415926535897932;

// cin,cout高速化のおまじない＋桁数指定
struct Fast {
  Fast() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(std::numeric_limits<double>::max_digits10);
  }
} fast;

#define REPS(i, S, E) for (ll i = (S); i <= (E); i++)
#define rep(i, S, E) for (ll i = (S); i <= (E); i++)
#define REP(i, N) REPS(i, 0, (N)-1)
#define DEPS(i, S, E) for (ll i = (E); i >= (S); i--)
#define dep(i, E, S) for (ll i = (E); i >= (S); i--)
#define DEP(i, N) DEPS(i, 0, (N)-1)
#define EACH(e, v) for (auto &&e : v)
#define each(e, v) for (auto &&e : v)
#define ALL(v) (v).begin(), (v).end()
#define RALL(v) (v).rbegin(), (v).rend()

template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline T MaxE(vector<T> &v, ll S, ll E) {
  T m = v[S];
  REPS(i, S, E) chmax(m, v[i]);
  return m;
} // v[S]～v[E]の最大値
template <class T> inline T MinE(vector<T> &v, ll S, ll E) {
  T m = v[S];
  REPS(i, S, E) chmin(m, v[i]);
  return m;
} // v[S]～v[E]の最小値
template <class T> inline T MaxE(vector<T> &v, ll N) {
  return MaxE(v, 0, N - 1);
} // 先頭N個中の最大値
template <class T> inline T MinE(vector<T> &v, ll N) {
  return MinE(v, 0, N - 1);
}
template <class T> inline T MaxE(vector<T> &v) { return MaxE(v, (ll)v.size()); }
template <class T> inline T MinE(vector<T> &v) { return MinE(v, (ll)v.size()); }
template <class T> inline ll MaxI(vector<T> &v, ll S, ll E) {
  ll m = S;
  REPS(i, S, E) {
    if (v[i] > v[m])
      m = i;
  }
  return m;
}
template <class T> inline ll MinI(vector<T> &v, ll S, ll E) {
  ll m = S;
  REPS(i, S, E) {
    if (v[i] < v[m])
      m = i;
  }
  return m;
}
template <class T> inline ll MaxI(vector<T> &v, ll N) {
  return MaxI(v, 0, N - 1);
}
template <class T> inline ll MinI(vector<T> &v, ll N) {
  return MinI(v, 0, N - 1);
}
template <class T> inline ll MaxI(vector<T> &v) {
  return MaxI(v, (ll)v.size());
}
template <class T> inline ll MinI(vector<T> &v) {
  return MinI(v, (ll)v.size());
}
template <class T> inline T Sum(vector<T> &v, ll S, ll E) {
  T s = v[S];
  REPS(i, S + 1, E) s += v[i];
  return s;
}
template <class T> inline T Sum(vector<T> &v, ll N) { return Sum(v, 0, N - 1); }
template <class T> inline T Sum(vector<T> &v) { return Sum(v, v.size()); }
template <class T> inline ll sz(T &v) { return (ll)v.size(); }
template <class T> inline T POW(T a, ll n) {
  T r = 1;
  for (; n > 0; n >>= 1, a *= a) {
    if (n & 1)
      r *= a;
  }
  return r;
}
inline ll POW(int a, ll n) { return POW((ll)a, n); }
inline ll CEIL(ll a, ll b) { return (a + b - 1) / b; }
ll Gcd(ll a, ll b) { return (b == 0) ? a : Gcd(b, a % b); }
ll Lcm(ll a, ll b) { return a * b / Gcd(a, b); }
inline ll MSB(ll a) {
  for (ll o = 63, x = -1;;) {
    ll m = (o + x) / 2;
    if (a < (1LL << m))
      o = m;
    else
      x = m;
    if (o - x == 1)
      return x;
  }
}
inline ll Upper2N(ll s) { return 1LL << MSB(s) << 1; } // s<2^nなる最小の2^n
inline vll Bit2Idx(ll m) {
  vll v;
  for (ll i = 0; m; m >>= 1, i++)
    if (m & 1)
      v.push_back(i);
  return move(v);
}
inline ll BitNum(ll m) {
  for (ll c = 0;; m >>= 1) {
    c += m & 1;
    if (!m)
      return c;
  }
}
inline ll Bit(ll s, ll i) { return (s >> i) & 1; } // sの第ibit i=0-63
[[nodiscard]] inline ll BitOn(ll s, ll i) {
  return s | (1LL << i);
} // sの第ibitON i=0-63
[[nodiscard]] inline ll BitOff(ll s, ll i) {
  return s & ~(1LL << i);
} // sの第ibitOFF i=0-63
[[nodiscard]] inline ll BitCut(ll s, ll i) {
  return s & (1LL << ++i) - 1;
} // sの第0～第ibitを抽出
inline vll str2num(string &s, ll N) {
  vll v(N);
  REP(i, N) v[i] = (ll)(s[i] - '0');
  return move(v);
}
inline vll ALP2num(string &s, ll N) {
  vll v(N);
  REP(i, N) v[i] = (ll)(s[i] - 'A');
  return move(v);
}
inline vll alp2num(string &s, ll N) {
  vll v(N);
  REP(i, N) v[i] = (ll)(s[i] - 'a');
  return move(v);
}
template <class T> inline ll FloorIdx(vector<T> &v, T x) {
  return upper_bound(ALL(v), x) - v.begin() - 1;
}
template <class T> inline ll CeilIdx(vector<T> &v, T x) {
  return lower_bound(ALL(v), x) - v.begin();
}
template <class T>
inline ll UnderNumOf(vector<T> &v, T x) { // sort済vのx以下の個数を得る
  return upper_bound(v.begin(), v.end(), x) - v.begin();
}
template <class T, class Pr>
inline ll UnderNumOf(vector<T> &v, T x, Pr pred) { // x以下個数
  return upper_bound(v.begin(), v.end(), x, pred) - v.begin();
}
template <class T>
inline ll OverNumOf(vector<T> &v, T x) { // sort済vのx以上の個数を得る
  return (ll)v.size() - (lower_bound(v.begin(), v.end(), x) - v.begin());
}
template <class T, class Pr>
inline ll OverNumOf(vector<T> &v, T x, Pr pred) { // x以上の個数
  return (ll)v.size() - (lower_bound(v.begin(), v.end(), x, pred) - v.begin());
}

template <class T = ll> inline vector<T> cinv(ll N) {
  vector<T> v(N);
  REP(i, N) cin >> v[i];
  return move(v);
}
template <class T = ll, class S = ll> inline vector<pair<T, S>> cinv2(ll N) {
  vector<pair<T, S>> v(N);
  REP(i, N) { cin >> v[i].first >> v[i].second; }
  return move(v);
}
template <class T = ll, class S = ll, class R = ll>
inline vector<tuple<T, S, R>> cinv3(ll N) {
  vector<tuple<T, S, R>> v(N);
  REP(i, N) { cin >> get<0>(v[i]) >> get<1>(v[i]) >> get<2>(v[i]); }
  return move(v);
}
template <class T = ll, class S = ll, class R = ll, class Q = ll>
inline vector<tuple<T, S, R, Q>> cinv4(ll N) {
  vector<tuple<T, S, R, Q>> v(N);
  REP(i, N) {
    cin >> get<0>(v[i]) >> get<1>(v[i]) >> get<2>(v[i]) >> get<3>(v[i]);
  }
  return move(v);
}
template <class T = ll> inline vector<vector<T>> cinvv(ll N, ll M) {
  vector<vector<T>> vv(N);
  REP(i, N) vv[i] = cinv(M);
  return move(vv);
}
template <class T> inline void coutv(vector<T> &v, string d = " ") {
  ll N = (ll)v.size();
  REP(i, N) { cout << v[i] << ((i == N - 1) ? "" : d); }
  cout << '\\n';
}
template <class T> inline void coutv(deque<T> &v, string d = " ") {
  ll N = (ll)v.size();
  REP(i, N) { cout << v[i] << ((i == N - 1) ? "" : d); }
  cout << '\\n';
}
template <class T> void bye(T a) {
  cout << a << '\\n';
  exit(0);
}

#if defined(_DEBUG)
ll dumpW = 5;
template <class T> void Dump(vector<T> &v) {
  REP(i, (ll)v.size()) {
    cerr << ((i == 0) ? "[" : " ") << setw(dumpW) << v[i];
  }
  cerr << "]";
}
void Dump(vll &v) {
  REP(i, (ll)v.size()) {
    cerr << ((i == 0) ? "[" : " ") << setw(dumpW);
    if (v[i] == INF)
      cerr << "INF";
    else if (v[i] == -INF)
      cerr << "-INF";
    else
      cerr << v[i];
  }
  cerr << "]";
}
template <class T> void Dump(vector<vector<T>> &v) {
  ll N = (ll)v.size();
  string d[2][2] = {{" ", "["}, {"\\n", "]\\n"}};
  REP(i, N) {
    cerr << d[0][i == 0];
    Dump(v[i]);
    cerr << d[1][i == N - 1];
  }
}
template <class T> void Dump(vector<vector<vector<T>>> &v) {
  ll N = (ll)v.size();
  string d[2] = {"  <", "[ <"};
  REP(i, N) {
    cerr << d[i == 0] << i << ">\\n";
    Dump(v[i]);
  }
  cerr << "]\\n";
}
template <class T> void Dump(vector<vector<vector<vector<T>>>> &v) {
  ll N = (ll)v.size();
  string d[2] = {"  ---<", "[ ---<"};
  REP(i, N) {
    cerr << d[i == 0] << i << ">---\\n";
    Dump(v[i]);
  }
  cerr << "]\\n";
}
template <class T> void Dump(vector<vector<vector<vector<vector<T>>>>> &v) {
  ll N = (ll)v.size();
  string d[2] = {"  ======<", "[ ======<"};
  REP(i, N) {
    cerr << d[i == 0] << i << ">======\\n";
    Dump(v[i]);
  }
  cerr << "]\\n";
}
#else
template <class T> void Dump(vector<T> &v) {}
template <class T> void Dump(vector<vector<T>> &v) {}
template <class T> void Dump(vector<vector<vector<T>>> &v) {}
template <class T> void Dump(vector<vector<vector<vector<T>>>> &v) {}
template <class T> void Dump(vector<vector<vector<vector<vector<T>>>>> &v) {}
#endif

template <ll MOD> struct mll_ {
  ll val;
  mll_(ll v = 0) : val(v % MOD) {
    if (val < 0)
      val += MOD;
  }
  mll_ operator-() const { return -val; }
  mll_ operator+(const mll_ &b) const { return val + b.val; }
  mll_ operator-(const mll_ &b) const { return val - b.val; }
  mll_ operator*(const mll_ &b) const { return val * b.val; }
  mll_ operator/(const mll_ &b) const { return mll_(*this) /= b; }
  mll_ operator+(ll b) const { return *this + mll_(b); }
  mll_ operator-(ll b) const { return *this - mll_(b); }
  mll_ operator*(ll b) const { return *this * mll_(b); }
  friend mll_ operator+(ll a, const mll_ &b) { return b + a; }
  friend mll_ operator-(ll a, const mll_ &b) { return -b + a; }
  friend mll_ operator*(ll a, const mll_ &b) { return b * a; }
  friend mll_ operator/(ll a, const mll_ &b) { return mll_(a) / b; }
  mll_ &operator+=(const mll_ &b) {
    val = (val + b.val) % MOD;
    return *this;
  }
  mll_ &operator-=(const mll_ &b) {
    val = (val + MOD - b.val) % MOD;
    return *this;
  }
  mll_ &operator*=(const mll_ &b) {
    val = (val * b.val) % MOD;
    return *this;
  }
  mll_ &operator/=(const mll_ &b) {
    ll c = b.val, d = MOD, u = 1, v = 0;
    while (d) {
      ll t = c / d;
      c -= t * d;
      swap(c, d);
      u -= t * v;
      swap(u, v);
    }
    val = val * u % MOD;
    if (val < 0)
      val += MOD;
    return *this;
  }
  mll_ &operator+=(ll b) { return *this += mll_(b); }
  mll_ &operator-=(ll b) { return *this -= mll_(b); }
  mll_ &operator*=(ll b) { return *this *= mll_(b); }
  mll_ &operator/=(ll b) { return *this /= mll_(b); }
  bool operator==(const mll_ &b) { return val == b.val; }
  bool operator!=(const mll_ &b) { return val != b.val; }
  bool operator==(ll b) { return *this == mll_(b); }
  bool operator!=(ll b) { return *this != mll_(b); }
  friend bool operator==(ll a, const mll_ &b) { return mll_(a) == b.val; }
  friend bool operator!=(ll a, const mll_ &b) { return mll_(a) != b.val; }
  friend ostream &operator<<(ostream &os, const mll_ &a) { return os << a.val; }
  friend istream &operator>>(istream &is, mll_ &a) { return is >> a.val; }
  static mll_ Combination(ll a, ll b) {
    chmin(b, a - b);
    if (b < 0)
      return mll_(0);
    mll_ c = 1;
    REP(i, b) c *= a - i;
    REP(i, b) c /= i + 1;
    return c;
  }
};
using mll = mll_<1000000007LL>; // 1000000007LL;// 998244353LL;
using vmll = std::vector<mll>;
using vvmll = std::vector<vmll>;
using vvvmll = std::vector<vvmll>;
using vvvvmll = std::vector<vvvmll>;
using vvvvvmll = std::vector<vvvvmll>;

pair<vll, vector<bool>> eratosthenes(ll n) {
  vll primes;
  vector<bool> table(n + 1);
  table[0] = table[1] = true;
  rep(i, 2, n) {
    if (table[i])
      continue;
    primes.push_back(i);
    for (ll j = 2; i * j <= n; j++)
      table[i * j] = true;
  }
  return move(make_pair(move(primes), move(table)));
}

void solve() {
  ll n;
  cin >> n;
  vll primes;
  vector<bool> ptable;
  tie(primes, ptable) = eratosthenes(n);
  ll m = sz(primes);

  ll ans = 1;
  rep(k, 2, n) {
    if (!ptable[k]) { // 素数なら
      ans += k * 2;
      continue;
    }

    ll r = k;

    ll val = k;
    rep(i, 0, m - 1) {
      ll p = primes[i];
      if (p * p > val)
        break;

      ll ee = 0;
      while (true) {
        if (val % p > 0)
          break;
        ee++;
        val /= p;
      }
      r *= (ee + 1);

      if (val == 1)
        break;

      if (!ptable[val]) { // 素数
        r *= 2;
        break;
      }
    }
    ans += r;
  }
  cout << ans << '\\n';
}

int main() {
#if 1
  solve();
#else
  ll t;
  cin >> t;
  rep(i, 0, t - 1) { solve(); }
#endif
  return 0;
}