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

/*
 * じょえチャンネル
 * 高評価・チャンネル登録よろしくおねがいします！
 * https://www.youtube.com/channel/UCRXsI3FL_kvaVL9zoolBfbQ
 */

#include <bits/stdc++.h>

// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")

// here!!!
//  define int long long !!!!!

#define int long long

// define int long long !!!!!

#define mod (int)((1e9) + 7)
// constexpr int mod = 998244353ll;

#ifdef int
#define inf (int)(3e18)
#else
#define inf (int)(5e8)
#endif

#define intt long long
#define itn long long
#define P pair<long long, long long>

#define rep(i, n) for (int i = 0; i < n; i++)
#define REP(i, n) for (int i = 1; i <= n; i++)
#define rev_rep(i, n) for (int i = n - 1; i >= 0; i--)
#define REV_REP(i, n) for (int i = n; i >= 1; i--)

#define ALL(v) v.begin(), v.end()

#define smallpriority_queue(x) priority_queue<x, vector<x>, greater<x>>

using namespace std;

// Library
// モッドパウ
inline int modpow(int x, int y, int m = mod) {
  int res = 1;
  while (y) {
    if (y & 1) {
      res *= x;
      res %= m;
    }
    x = x * x % m;
    y /= 2;
  }
  return res;
}

int mypow(int x, int y) {
  int res = 1;
  while (y) {
    if (y % 2) {
      res *= x;
    }
    x = x * x;
    y /= 2;
  }
  return res;
}
// is the number (x) a prime number?
bool prime(int x) {
  if (!x || x == 1) {
    return false;
  }
  for (int i = 2; i * i <= x; i++) {
    if (!(x % i)) {
      return false;
    }
  }
  return true;
}

// saidai-kouyakusuu
inline int gcd(int x, int y) {
  if (!y) {
    return x;
  }
  return gcd(y, x % y);
}

// number of keta
int keta(int x) {
  int ans = 0;
  while (x) {
    x /= 10;
    ans++;
  }
  return ans;
}

// sum of keta
int ketasum(int x) {
  int ans = 0;
  while (x) {
    ans += x % 10;
    x /= 10;
  }
  return ans;
}

inline int lcm(int x, int y) {
  int ans = x / gcd(x, y) * y;
  return ans;
}
int twobeki(int x) {
  int ans = 0;
  while (1) {
    if (!(x & 1)) {
      ans++;
      x >>= 1;
    } else {
      break;
    }
  }
  return ans;
}

template <class T, class U> inline bool chmax(T &lhs, const U &rhs) {
  if (lhs < rhs) {
    lhs = rhs;
    return 1;
  }
  return 0;
}
template <class T, class U> inline bool chmin(T &lhs, const U &rhs) {
  if (lhs > rhs) {
    lhs = rhs;
    return 1;
  }
  return 0;
}
void Yes() { cout << "Yes" << endl; }
void No() { cout << "No" << endl; }
void YES() { cout << "YES" << endl; }
void NO() { cout << "NO" << endl; }

#define fin(i) scanf("%lld", &i)
#define fout(i) printf("%lld", i)
#define fendl printf("\\n")

int kai(int x, int y) {
  int res = 1;
  for (int i = x - y + 1; i <= x; i++) {
    res *= i;
    res %= mod;
  }
  return res;
}

int comb(int x, int y) {
  if (y > x)
    return 0;
  //    cout<<kai(x, y)<<' '<<modpow(kai(y, y), mod - 2)<<endl;
  return kai(x, y) * modpow(kai(y, y), mod - 2) % mod;
}
// Library-End

#define vecin(v)                                                               \\
  for (int i = 0; i < v.size(); i++)                                           \\
    scanf("%lld", &v[i]);
#define vecout(v)                                                              \\
  {                                                                            \\
    for (int i = 0; i < (int)v.size(); i++)                                    \\
      printf("%lld ", v[i]);                                                   \\
    printf("\\n");                                                              \\
  }

template <typename T> class kaageSegTree {
protected:
  unsigned int n = 1, rank = 0;
  std::vector<T> node;
  T nodee;
  virtual T nodef(const T &, const T &) const = 0;

public:
  kaageSegTree(unsigned int m, T init, T nodee) : nodee(nodee) {
    while (n < m) {
      n *= 2;
      rank++;
    }
    node.resize(2 * n);
    for (unsigned int i = n; i < 2 * n; i++)
      node[i] = init;
  }
  kaageSegTree(const std::vector<T> &initvec, T nodee) : nodee(nodee) {
    unsigned int m = initvec.size();
    while (n < m) {
      n *= 2;
      rank++;
    }
    node.resize(2 * n);
    for (unsigned int i = n; i < 2 * n; i++) {
      if (i - n < m)
        node[i] = initvec[i - n];
    }
  }
  virtual void update(int i, T x) {
    i += n;
    node[i] = x;
    while (i != 1) {
      i >>= 1;
      node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
  }
  virtual T query(int l, int r) {
    l += n;
    r += n;
    T ls = nodee, rs = nodee;
    while (l < r) {
      if (l & 1) {
        ls = nodef(ls, node[l]);
        l++;
      }
      if (r & 1) {
        r--;
        rs = nodef(node[r], rs);
      }
      l >>= 1;
      r >>= 1;
    }
    return nodef(ls, rs);
  }
  virtual T operator[](const int &x) { return node[n + x]; }
  void fill(T x) { std::fill(ALL(node), x); }
  void print() {
    rep(i, n) std::cout << operator[](i) << " ";
    std::cout << std::endl;
  }
};
class RSQ : public kaageSegTree<int> {
  int nodef(const int &lhs, const int &rhs) const { return lhs + rhs; }

public:
  RSQ(int size, const int &def = 0) : kaageSegTree<int>(size, def, 0) {}
  RSQ(const std::vector<int> &initvec) : kaageSegTree<int>(initvec, 0) {}
};
class RMiQ : public kaageSegTree<int> {
  int nodef(const int &lhs, const int &rhs) const { return std::min(lhs, rhs); }

public:
  RMiQ(int size, const int &def = 0) : kaageSegTree<int>(size, def, inf) {}
  RMiQ(const std::vector<int> &initvec) : kaageSegTree<int>(initvec, inf) {}
};
class RMaQ : public kaageSegTree<int> {
  int nodef(const int &lhs, const int &rhs) const { return std::max(lhs, rhs); }

public:
  RMaQ(int size, const int &def = 0) : kaageSegTree<int>(size, def, -inf) {}
  RMaQ(const std::vector<int> &initvec) : kaageSegTree<int>(initvec, -inf) {}
};
template <typename T, typename U>
class IntervalSegTree : public kaageSegTree<T> {
protected:
  using kaageSegTree<T>::n;
  using kaageSegTree<T>::rank;
  using kaageSegTree<T>::node;
  using kaageSegTree<T>::nodef;
  using kaageSegTree<T>::nodee;
  std::vector<U> lazy;
  std::vector<bool> lazyflag;
  std::vector<int> width;
  virtual void lazyf(U &, const U &) = 0;
  virtual void updf(T &, const U &, const unsigned int &) = 0;
  void eval(int k) {
    for (int i = rank; i > 0; i--) {
      int nk = k >> i;
      if (lazyflag[nk]) {
        updf(node[2 * nk], lazy[nk], width[2 * nk]);
        updf(node[2 * nk + 1], lazy[nk], width[2 * nk + 1]);
        if (lazyflag[2 * nk])
          lazyf(lazy[2 * nk], lazy[nk]);
        else
          lazy[2 * nk] = lazy[nk];
        if (lazyflag[2 * nk + 1])
          lazyf(lazy[2 * nk + 1], lazy[nk]);
        else
          lazy[2 * nk + 1] = lazy[nk];
        lazyflag[2 * nk] = lazyflag[2 * nk + 1] = true;
        lazyflag[nk] = false;
      }
    }
  }

public:
  IntervalSegTree(unsigned int m, T init, T nodee)
      : kaageSegTree<T>(m, init, nodee) {
    lazy.resize(2 * n);
    lazyflag.resize(2 * n);
    width.resize(2 * n);
    width[1] = n;
    for (unsigned int i = 2; i < 2 * n; i++) {
      width[i] = width[i >> 1] >> 1;
    }
  }
  IntervalSegTree(T nodee, const std::vector<T> &initvec)
      : kaageSegTree<T>(initvec, nodee) {
    lazy.resize(2 * n);
    lazyflag.resize(2 * n);
    width.resize(2 * n);
    width[1] = n;
    for (unsigned int i = 2; i < 2 * n; i++) {
      width[i] = width[i >> 1] >> 1;
    }
  }
  void update(int i, U x) {
    i += n;
    eval(i);
    updf(node[i], x, width[i]);
    if (lazyflag[i])
      lazyf(lazy[i], x);
    else {
      lazyflag[i] = true;
      lazy[i] = x;
    }
    while (i /= 2)
      node[i] = nodef(node[2 * i], node[2 * i + 1]);
  }
  void update(int l, int r, U x) {
    l += n;
    r += n;
    int nl = l, nr = r;
    while (!(nl & 1))
      nl >>= 1;
    while (!(nr & 1))
      nr >>= 1;
    nr--;
    eval(nl);
    eval(nr);
    while (l < r) {
      if (l & 1) {
        updf(node[l], x, width[l]);
        if (lazyflag[l])
          lazyf(lazy[l], x);
        else {
          lazyflag[l] = true;
          lazy[l] = x;
        }
        l++;
      }
      if (r & 1) {
        r--;
        updf(node[r], x, width[r]);
        if (lazyflag[r])
          lazyf(lazy[r], x);
        else {
          lazyflag[r] = true;
          lazy[r] = x;
        }
      }
      l >>= 1;
      r >>= 1;
    }
    while (nl >>= 1)
      node[nl] = nodef(node[2 * nl], node[2 * nl + 1]);
    while (nr >>= 1)
      node[nr] = nodef(node[2 * nr], node[2 * nr + 1]);
  }
  T query(int l, int r) {
    l += n;
    r += n;
    eval(l);
    eval(r - 1);
    int ls = nodee, rs = nodee;
    while (l < r) {
      if (l & 1) {
        ls = nodef(ls, node[l]);
        l++;
      }
      if (r & 1) {
        r--;
        rs = nodef(node[r], rs);
      }
      l >>= 1;
      r >>= 1;
    }
    return nodef(ls, rs);
  }
  T operator[](const int &x) {
    eval(n + x);
    return node[n + x];
  }
  T queryForAll() { return node[1]; }
};
class RAQRSQ : public IntervalSegTree<int, int> {
  int nodef(const int &a, const int &b) const { return a + b; }
  void lazyf(int &a, const int &b) { a += b; }
  void updf(int &a, const int &b, const unsigned int &width) { a += width * b; }

public:
  RAQRSQ(int size, const int &def = 0)
      : IntervalSegTree<int, int>(size, def, 0) {
    for (int i = n - 1; i > 0; i--)
      node[i] = nodef(node[2 * i], node[2 * i + 1]);
  }
  RAQRSQ(const std::vector<int> &initvec)
      : IntervalSegTree<int, int>((int)0, initvec) {
    for (int i = n - 1; i > 0; i--)
      node[i] = nodef(node[2 * i], node[2 * i + 1]);
  }
};
class RAQRMiQ : public IntervalSegTree<int, int> {
  int nodef(const int &a, const int &b) const { return std::min(a, b); }
  void lazyf(int &a, const int &b) { a += b; }
  void updf(int &a, const int &b, const unsigned int &width) { a += b; }

public:
  RAQRMiQ(int size, const int &def = 0)
      : IntervalSegTree<int, int>(size, def, inf) {
    for (int i = n - 1; i > 0; i--)
      node[i] = nodef(node[2 * i], node[2 * i + 1]);
  }
  RAQRMiQ(const std::vector<int> &initvec)
      : IntervalSegTree<int, int>(inf, initvec) {
    for (int i = n - 1; i > 0; i--)
      node[i] = nodef(node[2 * i], node[2 * i + 1]);
  }
};
class RAQRMaQ : public IntervalSegTree<int, int> {
  int nodef(const int &a, const int &b) const { return std::max(a, b); }
  void lazyf(int &a, const int &b) { a += b; }
  void updf(int &a, const int &b, const unsigned int &width) { a += b; }

public:
  RAQRMaQ(unsigned int size, const int &def = 0)
      : IntervalSegTree<int, int>(size, def, -inf) {
    for (int i = n - 1; i > 0; i--)
      node[i] = nodef(node[2 * i], node[2 * i + 1]);
  }
  RAQRMaQ(const std::vector<int> &initvec)
      : IntervalSegTree<int, int>(-inf, initvec) {
    for (int i = n - 1; i > 0; i--)
      node[i] = nodef(node[2 * i], node[2 * i + 1]);
  }
};
class RUQRSQ : public IntervalSegTree<int, int> {
  int nodef(const int &a, const int &b) const { return a + b; }
  void lazyf(int &a, const int &b) { a = b; }
  void updf(int &a, const int &b, const unsigned int &width) { a = width * b; }

public:
  RUQRSQ(int size, const int &def = 0)
      : IntervalSegTree<int, int>(size, def, 0) {
    for (int i = n - 1; i > 0; i--)
      node[i] = nodef(node[2 * i], node[2 * i + 1]);
  }
  RUQRSQ(const std::vector<int> &initvec)
      : IntervalSegTree<int, int>((int)0, initvec) {
    for (int i = n - 1; i > 0; i--)
      node[i] = nodef(node[2 * i], node[2 * i + 1]);
  }
};
class RUQRMiQ : public IntervalSegTree<int, int> {
  int nodef(const int &a, const int &b) const { return std::min(a, b); }
  void lazyf(int &a, const int &b) { a = b; }
  void updf(int &a, const int &b, const unsigned int &width) { a = b; }

public:
  RUQRMiQ(int size, const int &def = 0)
      : IntervalSegTree<int, int>(size, def, inf) {
    for (int i = n - 1; i > 0; i--)
      node[i] = nodef(node[2 * i], node[2 * i + 1]);
  }
  RUQRMiQ(const std::vector<int> &initvec)
      : IntervalSegTree<int, int>(inf, initvec) {
    for (int i = n - 1; i > 0; i--)
      node[i] = nodef(node[2 * i], node[2 * i + 1]);
  }
};
class RUQRMaQ : public IntervalSegTree<int, int> {
  int nodef(const int &a, const int &b) const { return std::max(a, b); }
  void lazyf(int &a, const int &b) { a = b; }
  void updf(int &a, const int &b, const unsigned int &width) { a = b; }

public:
  RUQRMaQ(int size, const int &def = 0)
      : IntervalSegTree<int, int>(size, def, -inf) {
    for (int i = n - 1; i > 0; i--)
      node[i] = nodef(node[2 * i], node[2 * i + 1]);
  }
  RUQRMaQ(const std::vector<int> &initvec)
      : IntervalSegTree<int, int>(-inf, initvec) {
    for (int i = n - 1; i > 0; i--)
      node[i] = nodef(node[2 * i], node[2 * i + 1]);
  }
};

////SegTree
// template <class T>
// class SegTree {
//     int n;                       // 葉の数
//     vector<T> node;              // データを格納するvector
//     T def;                       // 初期値かつ単位元
//     function<T(T, T)> operation; // 区間クエリで使う処理
//     function<T(T, T)> update;    // 点更新で使う処理
//
//     // 区間[a,b)の総和。ノードk=[l,r)に着目している。
//     T _query(int a, int b, int k, int l, int r) {
//         if (r <= a || b <= l) return def; // 交差しない
//         if (a <= l && r <= b)
//             return node[k]; // a,l,r,bの順で完全に含まれる
//         else {
//             T c1 = _query(a, b, 2 * k + 1, l, (l + r) / 2); // 左の子
//             T c2 = _query(a, b, 2 * k + 2, (l + r) / 2, r); // 右の子
//             return operation(c1, c2);
//         }
//     }
//
// public:
//     // _n:必要サイズ, _def:初期値かつ単位元, _operation:クエリ関数,
//     // _update:更新関数
//     SegTree(size_t _n, T _def, function<T(T, T)> _operation,
//             function<T(T, T)> _update)
//     : def(_def), operation(_operation), update(_update) {
//         n = 1;
//         while (n < _n) {
//             n *= 2;
//         }
//         node = vector<T>(2 * n , def);
//     }
//
//     // 場所i(0-indexed)の値をxで更新
//     void change(int i, T x) {
//         i += n - 1;
//         node[i] = update(node[i], x);
//         while (i > 0) {
//             i = (i - 1) / 2;
//             node[i] = operation(node[i * 2 + 1], node[i * 2 + 2]);
//         }
//     }
//
//     // [a, b)の区間クエリを実行
//     T query(int a, int b) {
//         return _query(a, b, 0, 0, n);
//     }
//
//     // 添字でアクセス
//     T operator[](int i) {
//         return node[i + n - 1];
//     }
// };

template <class T> class SegTree {
  int n;
  vector<T> node;
  T def;
  function<T(T, T)> operation;
  function<T(T, T)> update;

public:
  SegTree(unsigned int _n, T _def, function<T(T, T)> _operation,
          function<T(T, T)> _update)
      : def(_def), operation(_operation), update(_update) {
    n = 1;
    while (n < _n) {
      n *= 2;
    }
    node = vector<T>(n * 2, def);
  }
  SegTree(vector<int> &initvec, function<T(T, T)> _operation,
          function<T(T, T)> _update)
      : operation(_operation), update(_update) {
    n = 1;
    while (n < initvec.size()) {
      n *= 2;
    }
    node = vector<T>(n * 2, def);
    for (int i = n; i < n + initvec.size(); i++) {
      node[i] = initvec[i - n];
    }
    for (int i = n - 1; i >= 1; i--) {
      node[i] = operation(node[i * 2], node[i * 2 + 1]);
    }
  }
  void change(int i, T x) {
    i += n;
    node[i] = update(node[i], x);
    while (i >= 1) {
      i >>= 1;
      node[i] = operation(node[i * 2], node[i * 2 + 1]);
    }
  }
  T query(int l, int r) {
    l += n;
    r += n;
    T rx = def, lx = def;
    while (l < r) {
      if (l & 1) {
        lx = operation(lx, node[l]);
        l++;
      }
      if (r & 1) {
        r--;
        rx = operation(node[r], rx);
      }
      l >>= 1;
      r >>= 1;
    }
    return operation(lx, rx);
  }
  T operator[](const int &x) { return node[x - n]; }
  void fill(T x) { std::fill(ALL(node), x); }
  void print() {
    rep(i, n) std::cout << operator[](i) << " ";
    std::cout << std::endl;
  }
};

#define R_MIN ([](long long a, long long b) { return min(a, b); })
#define R_MAX ([](long long a, long long b) { return max(a, b); })
#define R_SUM ([](long long a, long long b) { return a + b; })

#define NORMAL_UPDATE ([](long long a, long long b) { return b; })
#define ADD_UPDATE ([](long long a, long long b) { return a + b; })
#define MINUS_UPDATE ([](long long a, long long b) { return a - b; }

class Union_Find {
  vector<int> par;
  vector<int> rankmy;
  vector<int> ookisa;

public:
  Union_Find(int size) {
    par = vector<int>(size);
    rankmy = vector<int>(size);
    ookisa = vector<int>(size);
    for (int i = 0; i < size; i++) {
      par[i] = i;
      ookisa[i] = 1;
    }
  }

  int find(int x) {
    if (par[x] == x) {
      return x;
    }
    return par[x] = find(par[x]);
  }

  void unite(int x, int y) {
    x = find(x);
    y = find(y);
    if (x == y) {
      return;
    }
    if (rankmy[x] < rankmy[y]) {
      par[x] = y;
      ookisa[y] += ookisa[x];
      ookisa[x] = 0;
    } else {
      par[y] = x;
      ookisa[x] += ookisa[y];
      ookisa[y] = 0;
      if (rankmy[x] == rankmy[y]) {
        rankmy[x]++;
      }
    }
  }
  int size(int i) {
    i = find(i);
    return ookisa[i];
  }
  bool same(int x, int y) { return find(x) == find(y); }
};

class BIT {
  vector<int> data;
  int size = 0;

public:
  BIT(int _size) {
    data = vector<int>(_size + 1);
    size = _size;
  }
  void add(int i, int x) {
    while (i <= size) {
      data[i] += x;
      i += i & -i;
    }
  }
  int sum(int i) {
    assert(i <= size);
    int s = 0;
    while (i > 0) {
      s += data[i];
      i -= i & -i;
    }
    return s;
  }
  int lower_bound(int x) {
    if (x <= 0) {
      return 0;
    } else {
      int i = 0;
      int r = 1;
      while (r < size)
        r = r << 1;
      for (int len = r; len > 0; len = len >> 1) {
        if (i + len < size && data[i + len] < x) {
          x -= data[i + len];
          i += len;
        }
      }
      return i + 1;
    }
  }
};

// Union-Find-End

int perm[2000005];
void init_perm() {
  perm[0] = 1;
  REP(i, 2000004) { perm[i] = perm[i - 1] * i % mod; }
}

int nCk(int x, int y) {
  if (y > x) {
    return 0;
  }
  return perm[x] * modpow(perm[x - y], mod - 2) % mod *
         modpow(perm[y], mod - 2) % mod;
}

double kyori(pair<int, int> f, pair<int, int> s) {
  double ans = 0;
  double t = fabs(f.first - s.first);
  double y = fabs(f.second - s.second);
  ans = sqrt(t * t + y * y);
  return ans;
}

inline string stringmax(string &x, string &y) {
  if (x.size() > y.size()) {
    return x;
  }
  if (x.size() < y.size()) {
    return y;
  }
  rep(i, x.size()) {
    if (x[i] > y[i]) {
      return x;
    }
    if (x[i] < y[i]) {
      return y;
    }
  }
  return x;
}

vector<int> RollingHash(string &s, string &t) {
  vector<int> ans;
  __int128 h = 0, hamod = 0, ki = 0, kim = 0, hikaku = 0, one = 0;
  one = 1;
  ki = 1000000007ll;
  hamod = (one << 61) - 1;
  kim = 1;
  rep(i, t.size()) {
    hikaku *= ki;
    h *= ki;
    kim *= ki;
    hikaku += t[i];
    h += s[i];
    hikaku %= hamod;
    h %= hamod;
    kim %= hamod;
  }
  rep(i, (int)s.size() - (int)t.size() + 1) {
    if (h == hikaku) {
      ans.emplace_back(i);
    }
    h *= ki;
    h %= hamod;
    h += s[i + (int)t.size()];
    h %= hamod;
    h += hamod;
    h -= s[i] * kim % hamod;
    h %= hamod;
  }
  return ans;
}
struct edge {
  int to;
  int length;
  edge(int _to, int _length) {
    to = _to;
    length = _length;
  }
};
vector<int> djkstra(vector<vector<edge>> &road, int start) {
  vector<int> kyo(road.size(), inf);
  smallpriority_queue(P) q;
  q.push({0, start});
  kyo[start] = 0;
  while (q.size()) {
    int x = q.top().second;
    itn now = q.top().first;
    q.pop();
    if (kyo[x] < now) {
      continue;
    }
    for (auto &i : road[x]) {
      if (kyo[i.to] > now + i.length) {
        kyo[i.to] = now + i.length;
        q.push({kyo[i.to], i.to});
      }
    }
  }
  return kyo;
}

#define endl "\\n" // interactive の時に注意！！！
#define printd cout << fixed << setprecision(10)

int n, m, k, l, ans;
bool did[10000004];
itn cnt[10000004];
signed main() {
  ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  cin >> n;
  fill(cnt, cnt + n + 1, 1);
  REP(i, n) {
    int ka = cnt[i];
    if (!did[i] && i != 1) {
      ka *= 2;
    }
    ans += ka * i;
    if (i == 1) {
      continue;
    }
    if (did[i] || i == 1) {
      continue;
    }
    for (int j = i; j <= n; j += i) {
      int k = j;
      int c = 0;
      while (!(k % i)) {
        k /= i;
        c++;
      }
      did[j] = 1;
      cnt[j] *= c + 1;
    }
  }
  cout << ans << endl;
}


Error: TLE

Fixed submission:

/*
 * じょえチャンネル
 * 高評価・チャンネル登録よろしくおねがいします！
 * https://www.youtube.com/channel/UCRXsI3FL_kvaVL9zoolBfbQ
 */

#include <bits/stdc++.h>

// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")

// here!!!
//  define int long long !!!!!

#define int long long

// define int long long !!!!!

#define mod (int)((1e9) + 7)
// constexpr int mod = 998244353ll;

#ifdef int
#define inf (int)(3e18)
#else
#define inf (int)(5e8)
#endif

#define intt long long
#define itn long long
#define P pair<long long, long long>

#define rep(i, n) for (int i = 0; i < n; i++)
#define REP(i, n) for (int i = 1; i <= n; i++)
#define rev_rep(i, n) for (int i = n - 1; i >= 0; i--)
#define REV_REP(i, n) for (int i = n; i >= 1; i--)

#define ALL(v) v.begin(), v.end()

#define smallpriority_queue(x) priority_queue<x, vector<x>, greater<x>>

using namespace std;

// Library
// モッドパウ
inline int modpow(int x, int y, int m = mod) {
  int res = 1;
  while (y) {
    if (y & 1) {
      res *= x;
      res %= m;
    }
    x = x * x % m;
    y /= 2;
  }
  return res;
}

int mypow(int x, int y) {
  int res = 1;
  while (y) {
    if (y % 2) {
      res *= x;
    }
    x = x * x;
    y /= 2;
  }
  return res;
}
// is the number (x) a prime number?
bool prime(int x) {
  if (!x || x == 1) {
    return false;
  }
  for (int i = 2; i * i <= x; i++) {
    if (!(x % i)) {
      return false;
    }
  }
  return true;
}

// saidai-kouyakusuu
inline int gcd(int x, int y) {
  if (!y) {
    return x;
  }
  return gcd(y, x % y);
}

// number of keta
int keta(int x) {
  int ans = 0;
  while (x) {
    x /= 10;
    ans++;
  }
  return ans;
}

// sum of keta
int ketasum(int x) {
  int ans = 0;
  while (x) {
    ans += x % 10;
    x /= 10;
  }
  return ans;
}

inline int lcm(int x, int y) {
  int ans = x / gcd(x, y) * y;
  return ans;
}
int twobeki(int x) {
  int ans = 0;
  while (1) {
    if (!(x & 1)) {
      ans++;
      x >>= 1;
    } else {
      break;
    }
  }
  return ans;
}

template <class T, class U> inline bool chmax(T &lhs, const U &rhs) {
  if (lhs < rhs) {
    lhs = rhs;
    return 1;
  }
  return 0;
}
template <class T, class U> inline bool chmin(T &lhs, const U &rhs) {
  if (lhs > rhs) {
    lhs = rhs;
    return 1;
  }
  return 0;
}
void Yes() { cout << "Yes" << endl; }
void No() { cout << "No" << endl; }
void YES() { cout << "YES" << endl; }
void NO() { cout << "NO" << endl; }

#define fin(i) scanf("%lld", &i)
#define fout(i) printf("%lld", i)
#define fendl printf("\\n")

int kai(int x, int y) {
  int res = 1;
  for (int i = x - y + 1; i <= x; i++) {
    res *= i;
    res %= mod;
  }
  return res;
}

int comb(int x, int y) {
  if (y > x)
    return 0;
  //    cout<<kai(x, y)<<' '<<modpow(kai(y, y), mod - 2)<<endl;
  return kai(x, y) * modpow(kai(y, y), mod - 2) % mod;
}
// Library-End

#define vecin(v)                                                               \\
  for (int i = 0; i < v.size(); i++)                                           \\
    scanf("%lld", &v[i]);
#define vecout(v)                                                              \\
  {                                                                            \\
    for (int i = 0; i < (int)v.size(); i++)                                    \\
      printf("%lld ", v[i]);                                                   \\
    printf("\\n");                                                              \\
  }

template <typename T> class kaageSegTree {
protected:
  unsigned int n = 1, rank = 0;
  std::vector<T> node;
  T nodee;
  virtual T nodef(const T &, const T &) const = 0;

public:
  kaageSegTree(unsigned int m, T init, T nodee) : nodee(nodee) {
    while (n < m) {
      n *= 2;
      rank++;
    }
    node.resize(2 * n);
    for (unsigned int i = n; i < 2 * n; i++)
      node[i] = init;
  }
  kaageSegTree(const std::vector<T> &initvec, T nodee) : nodee(nodee) {
    unsigned int m = initvec.size();
    while (n < m) {
      n *= 2;
      rank++;
    }
    node.resize(2 * n);
    for (unsigned int i = n; i < 2 * n; i++) {
      if (i - n < m)
        node[i] = initvec[i - n];
    }
  }
  virtual void update(int i, T x) {
    i += n;
    node[i] = x;
    while (i != 1) {
      i >>= 1;
      node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
  }
  virtual T query(int l, int r) {
    l += n;
    r += n;
    T ls = nodee, rs = nodee;
    while (l < r) {
      if (l & 1) {
        ls = nodef(ls, node[l]);
        l++;
      }
      if (r & 1) {
        r--;
        rs = nodef(node[r], rs);
      }
      l >>= 1;
      r >>= 1;
    }
    return nodef(ls, rs);
  }
  virtual T operator[](const int &x) { return node[n + x]; }
  void fill(T x) { std::fill(ALL(node), x); }
  void print() {
    rep(i, n) std::cout << operator[](i) << " ";
    std::cout << std::endl;
  }
};
class RSQ : public kaageSegTree<int> {
  int nodef(const int &lhs, const int &rhs) const { return lhs + rhs; }

public:
  RSQ(int size, const int &def = 0) : kaageSegTree<int>(size, def, 0) {}
  RSQ(const std::vector<int> &initvec) : kaageSegTree<int>(initvec, 0) {}
};
class RMiQ : public kaageSegTree<int> {
  int nodef(const int &lhs, const int &rhs) const { return std::min(lhs, rhs); }

public:
  RMiQ(int size, const int &def = 0) : kaageSegTree<int>(size, def, inf) {}
  RMiQ(const std::vector<int> &initvec) : kaageSegTree<int>(initvec, inf) {}
};
class RMaQ : public kaageSegTree<int> {
  int nodef(const int &lhs, const int &rhs) const { return std::max(lhs, rhs); }

public:
  RMaQ(int size, const int &def = 0) : kaageSegTree<int>(size, def, -inf) {}
  RMaQ(const std::vector<int> &initvec) : kaageSegTree<int>(initvec, -inf) {}
};
template <typename T, typename U>
class IntervalSegTree : public kaageSegTree<T> {
protected:
  using kaageSegTree<T>::n;
  using kaageSegTree<T>::rank;
  using kaageSegTree<T>::node;
  using kaageSegTree<T>::nodef;
  using kaageSegTree<T>::nodee;
  std::vector<U> lazy;
  std::vector<bool> lazyflag;
  std::vector<int> width;
  virtual void lazyf(U &, const U &) = 0;
  virtual void updf(T &, const U &, const unsigned int &) = 0;
  void eval(int k) {
    for (int i = rank; i > 0; i--) {
      int nk = k >> i;
      if (lazyflag[nk]) {
        updf(node[2 * nk], lazy[nk], width[2 * nk]);
        updf(node[2 * nk + 1], lazy[nk], width[2 * nk + 1]);
        if (lazyflag[2 * nk])
          lazyf(lazy[2 * nk], lazy[nk]);
        else
          lazy[2 * nk] = lazy[nk];
        if (lazyflag[2 * nk + 1])
          lazyf(lazy[2 * nk + 1], lazy[nk]);
        else
          lazy[2 * nk + 1] = lazy[nk];
        lazyflag[2 * nk] = lazyflag[2 * nk + 1] = true;
        lazyflag[nk] = false;
      }
    }
  }

public:
  IntervalSegTree(unsigned int m, T init, T nodee)
      : kaageSegTree<T>(m, init, nodee) {
    lazy.resize(2 * n);
    lazyflag.resize(2 * n);
    width.resize(2 * n);
    width[1] = n;
    for (unsigned int i = 2; i < 2 * n; i++) {
      width[i] = width[i >> 1] >> 1;
    }
  }
  IntervalSegTree(T nodee, const std::vector<T> &initvec)
      : kaageSegTree<T>(initvec, nodee) {
    lazy.resize(2 * n);
    lazyflag.resize(2 * n);
    width.resize(2 * n);
    width[1] = n;
    for (unsigned int i = 2; i < 2 * n; i++) {
      width[i] = width[i >> 1] >> 1;
    }
  }
  void update(int i, U x) {
    i += n;
    eval(i);
    updf(node[i], x, width[i]);
    if (lazyflag[i])
      lazyf(lazy[i], x);
    else {
      lazyflag[i] = true;
      lazy[i] = x;
    }
    while (i /= 2)
      node[i] = nodef(node[2 * i], node[2 * i + 1]);
  }
  void update(int l, int r, U x) {
    l += n;
    r += n;
    int nl = l, nr = r;
    while (!(nl & 1))
      nl >>= 1;
    while (!(nr & 1))
      nr >>= 1;
    nr--;
    eval(nl);
    eval(nr);
    while (l < r) {
      if (l & 1) {
        updf(node[l], x, width[l]);
        if (lazyflag[l])
          lazyf(lazy[l], x);
        else {
          lazyflag[l] = true;
          lazy[l] = x;
        }
        l++;
      }
      if (r & 1) {
        r--;
        updf(node[r], x, width[r]);
        if (lazyflag[r])
          lazyf(lazy[r], x);
        else {
          lazyflag[r] = true;
          lazy[r] = x;
        }
      }
      l >>= 1;
      r >>= 1;
    }
    while (nl >>= 1)
      node[nl] = nodef(node[2 * nl], node[2 * nl + 1]);
    while (nr >>= 1)
      node[nr] = nodef(node[2 * nr], node[2 * nr + 1]);
  }
  T query(int l, int r) {
    l += n;
    r += n;
    eval(l);
    eval(r - 1);
    int ls = nodee, rs = nodee;
    while (l < r) {
      if (l & 1) {
        ls = nodef(ls, node[l]);
        l++;
      }
      if (r & 1) {
        r--;
        rs = nodef(node[r], rs);
      }
      l >>= 1;
      r >>= 1;
    }
    return nodef(ls, rs);
  }
  T operator[](const int &x) {
    eval(n + x);
    return node[n + x];
  }
  T queryForAll() { return node[1]; }
};
class RAQRSQ : public IntervalSegTree<int, int> {
  int nodef(const int &a, const int &b) const { return a + b; }
  void lazyf(int &a, const int &b) { a += b; }
  void updf(int &a, const int &b, const unsigned int &width) { a += width * b; }

public:
  RAQRSQ(int size, const int &def = 0)
      : IntervalSegTree<int, int>(size, def, 0) {
    for (int i = n - 1; i > 0; i--)
      node[i] = nodef(node[2 * i], node[2 * i + 1]);
  }
  RAQRSQ(const std::vector<int> &initvec)
      : IntervalSegTree<int, int>((int)0, initvec) {
    for (int i = n - 1; i > 0; i--)
      node[i] = nodef(node[2 * i], node[2 * i + 1]);
  }
};
class RAQRMiQ : public IntervalSegTree<int, int> {
  int nodef(const int &a, const int &b) const { return std::min(a, b); }
  void lazyf(int &a, const int &b) { a += b; }
  void updf(int &a, const int &b, const unsigned int &width) { a += b; }

public:
  RAQRMiQ(int size, const int &def = 0)
      : IntervalSegTree<int, int>(size, def, inf) {
    for (int i = n - 1; i > 0; i--)
      node[i] = nodef(node[2 * i], node[2 * i + 1]);
  }
  RAQRMiQ(const std::vector<int> &initvec)
      : IntervalSegTree<int, int>(inf, initvec) {
    for (int i = n - 1; i > 0; i--)
      node[i] = nodef(node[2 * i], node[2 * i + 1]);
  }
};
class RAQRMaQ : public IntervalSegTree<int, int> {
  int nodef(const int &a, const int &b) const { return std::max(a, b); }
  void lazyf(int &a, const int &b) { a += b; }
  void updf(int &a, const int &b, const unsigned int &width) { a += b; }

public:
  RAQRMaQ(unsigned int size, const int &def = 0)
      : IntervalSegTree<int, int>(size, def, -inf) {
    for (int i = n - 1; i > 0; i--)
      node[i] = nodef(node[2 * i], node[2 * i + 1]);
  }
  RAQRMaQ(const std::vector<int> &initvec)
      : IntervalSegTree<int, int>(-inf, initvec) {
    for (int i = n - 1; i > 0; i--)
      node[i] = nodef(node[2 * i], node[2 * i + 1]);
  }
};
class RUQRSQ : public IntervalSegTree<int, int> {
  int nodef(const int &a, const int &b) const { return a + b; }
  void lazyf(int &a, const int &b) { a = b; }
  void updf(int &a, const int &b, const unsigned int &width) { a = width * b; }

public:
  RUQRSQ(int size, const int &def = 0)
      : IntervalSegTree<int, int>(size, def, 0) {
    for (int i = n - 1; i > 0; i--)
      node[i] = nodef(node[2 * i], node[2 * i + 1]);
  }
  RUQRSQ(const std::vector<int> &initvec)
      : IntervalSegTree<int, int>((int)0, initvec) {
    for (int i = n - 1; i > 0; i--)
      node[i] = nodef(node[2 * i], node[2 * i + 1]);
  }
};
class RUQRMiQ : public IntervalSegTree<int, int> {
  int nodef(const int &a, const int &b) const { return std::min(a, b); }
  void lazyf(int &a, const int &b) { a = b; }
  void updf(int &a, const int &b, const unsigned int &width) { a = b; }

public:
  RUQRMiQ(int size, const int &def = 0)
      : IntervalSegTree<int, int>(size, def, inf) {
    for (int i = n - 1; i > 0; i--)
      node[i] = nodef(node[2 * i], node[2 * i + 1]);
  }
  RUQRMiQ(const std::vector<int> &initvec)
      : IntervalSegTree<int, int>(inf, initvec) {
    for (int i = n - 1; i > 0; i--)
      node[i] = nodef(node[2 * i], node[2 * i + 1]);
  }
};
class RUQRMaQ : public IntervalSegTree<int, int> {
  int nodef(const int &a, const int &b) const { return std::max(a, b); }
  void lazyf(int &a, const int &b) { a = b; }
  void updf(int &a, const int &b, const unsigned int &width) { a = b; }

public:
  RUQRMaQ(int size, const int &def = 0)
      : IntervalSegTree<int, int>(size, def, -inf) {
    for (int i = n - 1; i > 0; i--)
      node[i] = nodef(node[2 * i], node[2 * i + 1]);
  }
  RUQRMaQ(const std::vector<int> &initvec)
      : IntervalSegTree<int, int>(-inf, initvec) {
    for (int i = n - 1; i > 0; i--)
      node[i] = nodef(node[2 * i], node[2 * i + 1]);
  }
};

////SegTree
// template <class T>
// class SegTree {
//     int n;                       // 葉の数
//     vector<T> node;              // データを格納するvector
//     T def;                       // 初期値かつ単位元
//     function<T(T, T)> operation; // 区間クエリで使う処理
//     function<T(T, T)> update;    // 点更新で使う処理
//
//     // 区間[a,b)の総和。ノードk=[l,r)に着目している。
//     T _query(int a, int b, int k, int l, int r) {
//         if (r <= a || b <= l) return def; // 交差しない
//         if (a <= l && r <= b)
//             return node[k]; // a,l,r,bの順で完全に含まれる
//         else {
//             T c1 = _query(a, b, 2 * k + 1, l, (l + r) / 2); // 左の子
//             T c2 = _query(a, b, 2 * k + 2, (l + r) / 2, r); // 右の子
//             return operation(c1, c2);
//         }
//     }
//
// public:
//     // _n:必要サイズ, _def:初期値かつ単位元, _operation:クエリ関数,
//     // _update:更新関数
//     SegTree(size_t _n, T _def, function<T(T, T)> _operation,
//             function<T(T, T)> _update)
//     : def(_def), operation(_operation), update(_update) {
//         n = 1;
//         while (n < _n) {
//             n *= 2;
//         }
//         node = vector<T>(2 * n , def);
//     }
//
//     // 場所i(0-indexed)の値をxで更新
//     void change(int i, T x) {
//         i += n - 1;
//         node[i] = update(node[i], x);
//         while (i > 0) {
//             i = (i - 1) / 2;
//             node[i] = operation(node[i * 2 + 1], node[i * 2 + 2]);
//         }
//     }
//
//     // [a, b)の区間クエリを実行
//     T query(int a, int b) {
//         return _query(a, b, 0, 0, n);
//     }
//
//     // 添字でアクセス
//     T operator[](int i) {
//         return node[i + n - 1];
//     }
// };

template <class T> class SegTree {
  int n;
  vector<T> node;
  T def;
  function<T(T, T)> operation;
  function<T(T, T)> update;

public:
  SegTree(unsigned int _n, T _def, function<T(T, T)> _operation,
          function<T(T, T)> _update)
      : def(_def), operation(_operation), update(_update) {
    n = 1;
    while (n < _n) {
      n *= 2;
    }
    node = vector<T>(n * 2, def);
  }
  SegTree(vector<int> &initvec, function<T(T, T)> _operation,
          function<T(T, T)> _update)
      : operation(_operation), update(_update) {
    n = 1;
    while (n < initvec.size()) {
      n *= 2;
    }
    node = vector<T>(n * 2, def);
    for (int i = n; i < n + initvec.size(); i++) {
      node[i] = initvec[i - n];
    }
    for (int i = n - 1; i >= 1; i--) {
      node[i] = operation(node[i * 2], node[i * 2 + 1]);
    }
  }
  void change(int i, T x) {
    i += n;
    node[i] = update(node[i], x);
    while (i >= 1) {
      i >>= 1;
      node[i] = operation(node[i * 2], node[i * 2 + 1]);
    }
  }
  T query(int l, int r) {
    l += n;
    r += n;
    T rx = def, lx = def;
    while (l < r) {
      if (l & 1) {
        lx = operation(lx, node[l]);
        l++;
      }
      if (r & 1) {
        r--;
        rx = operation(node[r], rx);
      }
      l >>= 1;
      r >>= 1;
    }
    return operation(lx, rx);
  }
  T operator[](const int &x) { return node[x - n]; }
  void fill(T x) { std::fill(ALL(node), x); }
  void print() {
    rep(i, n) std::cout << operator[](i) << " ";
    std::cout << std::endl;
  }
};

#define R_MIN ([](long long a, long long b) { return min(a, b); })
#define R_MAX ([](long long a, long long b) { return max(a, b); })
#define R_SUM ([](long long a, long long b) { return a + b; })

#define NORMAL_UPDATE ([](long long a, long long b) { return b; })
#define ADD_UPDATE ([](long long a, long long b) { return a + b; })
#define MINUS_UPDATE ([](long long a, long long b) { return a - b; }

class Union_Find {
  vector<int> par;
  vector<int> rankmy;
  vector<int> ookisa;

public:
  Union_Find(int size) {
    par = vector<int>(size);
    rankmy = vector<int>(size);
    ookisa = vector<int>(size);
    for (int i = 0; i < size; i++) {
      par[i] = i;
      ookisa[i] = 1;
    }
  }

  int find(int x) {
    if (par[x] == x) {
      return x;
    }
    return par[x] = find(par[x]);
  }

  void unite(int x, int y) {
    x = find(x);
    y = find(y);
    if (x == y) {
      return;
    }
    if (rankmy[x] < rankmy[y]) {
      par[x] = y;
      ookisa[y] += ookisa[x];
      ookisa[x] = 0;
    } else {
      par[y] = x;
      ookisa[x] += ookisa[y];
      ookisa[y] = 0;
      if (rankmy[x] == rankmy[y]) {
        rankmy[x]++;
      }
    }
  }
  int size(int i) {
    i = find(i);
    return ookisa[i];
  }
  bool same(int x, int y) { return find(x) == find(y); }
};

class BIT {
  vector<int> data;
  int size = 0;

public:
  BIT(int _size) {
    data = vector<int>(_size + 1);
    size = _size;
  }
  void add(int i, int x) {
    while (i <= size) {
      data[i] += x;
      i += i & -i;
    }
  }
  int sum(int i) {
    assert(i <= size);
    int s = 0;
    while (i > 0) {
      s += data[i];
      i -= i & -i;
    }
    return s;
  }
  int lower_bound(int x) {
    if (x <= 0) {
      return 0;
    } else {
      int i = 0;
      int r = 1;
      while (r < size)
        r = r << 1;
      for (int len = r; len > 0; len = len >> 1) {
        if (i + len < size && data[i + len] < x) {
          x -= data[i + len];
          i += len;
        }
      }
      return i + 1;
    }
  }
};

// Union-Find-End

int perm[2000005];
void init_perm() {
  perm[0] = 1;
  REP(i, 2000004) { perm[i] = perm[i - 1] * i % mod; }
}

int nCk(int x, int y) {
  if (y > x) {
    return 0;
  }
  return perm[x] * modpow(perm[x - y], mod - 2) % mod *
         modpow(perm[y], mod - 2) % mod;
}

double kyori(pair<int, int> f, pair<int, int> s) {
  double ans = 0;
  double t = fabs(f.first - s.first);
  double y = fabs(f.second - s.second);
  ans = sqrt(t * t + y * y);
  return ans;
}

inline string stringmax(string &x, string &y) {
  if (x.size() > y.size()) {
    return x;
  }
  if (x.size() < y.size()) {
    return y;
  }
  rep(i, x.size()) {
    if (x[i] > y[i]) {
      return x;
    }
    if (x[i] < y[i]) {
      return y;
    }
  }
  return x;
}

vector<int> RollingHash(string &s, string &t) {
  vector<int> ans;
  __int128 h = 0, hamod = 0, ki = 0, kim = 0, hikaku = 0, one = 0;
  one = 1;
  ki = 1000000007ll;
  hamod = (one << 61) - 1;
  kim = 1;
  rep(i, t.size()) {
    hikaku *= ki;
    h *= ki;
    kim *= ki;
    hikaku += t[i];
    h += s[i];
    hikaku %= hamod;
    h %= hamod;
    kim %= hamod;
  }
  rep(i, (int)s.size() - (int)t.size() + 1) {
    if (h == hikaku) {
      ans.emplace_back(i);
    }
    h *= ki;
    h %= hamod;
    h += s[i + (int)t.size()];
    h %= hamod;
    h += hamod;
    h -= s[i] * kim % hamod;
    h %= hamod;
  }
  return ans;
}
struct edge {
  int to;
  int length;
  edge(int _to, int _length) {
    to = _to;
    length = _length;
  }
};
vector<int> djkstra(vector<vector<edge>> &road, int start) {
  vector<int> kyo(road.size(), inf);
  smallpriority_queue(P) q;
  q.push({0, start});
  kyo[start] = 0;
  while (q.size()) {
    int x = q.top().second;
    itn now = q.top().first;
    q.pop();
    if (kyo[x] < now) {
      continue;
    }
    for (auto &i : road[x]) {
      if (kyo[i.to] > now + i.length) {
        kyo[i.to] = now + i.length;
        q.push({kyo[i.to], i.to});
      }
    }
  }
  return kyo;
}

#define endl "\\n" // interactive の時に注意！！！
#define printd cout << fixed << setprecision(10)

int n, m, k, l, ans;
bool did[10000004];
map<int, int> mp[10000004];
signed main() {
  ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  cin >> n;
  REP(i, n) {
    int ka = 1;
    if (!did[i] && i != 1) {
      ka *= 2;
    }
    for (auto &j : mp[i]) {
      ka *= j.second + 1;
    }
    map<int, int> k = mp[i];
    ans += ka * i;
    if (i == 1) {
      continue;
    }
    if (did[i] || i == 1) {
      continue;
    }
    for (int j = i; j <= n; j += i) {
      int k = j / i;
      itn c = 0;
      while (!(k % i)) {
        c++;
        k /= i;
      }
      did[j] = 1;
      mp[j][i] += c + 1;
    }
  }
  cout << ans << endl;
}