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

#include <algorithm>
#include <bitset>
#include <cassert>
#include <cfloat>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits.h>
#include <list>
#include <map>
#include <math.h>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
using namespace std;
#define int long long
#define ll long long
#define rep(i, n) for (ll i = 0; i < (n); i++)
#define P pair<ll, ll>
#define sz(x) (ll) x.size()
#define ALL(x) (x).begin(), (x).end()
#define ALLR(x) (x).rbegin(), (x).rend()
#define VE vector<ll>
#define COUT(x) cout << (x) << endl
#define MA map<ll, ll>
#define SE set<ll>
#define PQ priority_queue<ll>
#define PQR priority_queue<ll, VE, greater<ll>>
#define YES(n) cout << ((n) ? "YES" : "NO") << endl
#define Yes(n) cout << ((n) ? "Yes" : "No") << endl
#define EPS (1e-10)
#define pb push_back
long long MOD = 1000000007;
// long long MOD = 998244353;
const long long INF = 1LL << 60;
const long double PI = acos(-1.0);
struct mint {
  ll x; // typedef long long ll;
  mint(ll x = 0) : x((x % MOD + MOD) % MOD) {}
  mint operator-() const { return mint(-x); }
  mint &operator+=(const mint a) {
    if ((x += a.x) >= MOD)
      x -= MOD;
    return *this;
  }
  mint &operator-=(const mint a) {
    if ((x += MOD - a.x) >= MOD)
      x -= MOD;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= MOD;
    return *this;
  }
  mint operator+(const mint a) const {
    mint res(*this);
    return res += a;
  }
  mint operator-(const mint a) const {
    mint res(*this);
    return res -= a;
  }
  mint operator*(const mint a) const {
    mint res(*this);
    return res *= a;
  }
  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }
  // for prime MOD
  mint inv() const { return pow(MOD - 2); }
  mint &operator/=(const mint a) { return (*this) *= a.inv(); }
  mint operator/(const mint a) const {
    mint res(*this);
    return res /= a;
  }
  bool operator==(const mint a) const { return x == a.x; }
  bool operator!=(const mint a) const { return x != a.x; }
};
istream &operator>>(istream &is, const mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }
struct Sieve {
  int n;
  vector<int> f, primes;

  Sieve(int n = 1) : n(n), f(n + 1) {
    f[0] = f[1] = -1;
    for (ll i = 2; i <= n; ++i) {
      if (f[i])
        continue;
      primes.push_back(i);
      f[i] = i;
      for (ll j = i * i; j <= n; j += i) {
        if (!f[j])
          f[j] = i;
      }
    }
  }

  bool isPrime(int x) { return f[x] == x; }

  vector<int> factorList(int x) {
    vector<int> res;
    while (x != 1) {
      res.push_back(f[x]);
      x /= f[x];
    }
    return res;
  }

  vector<P> factor(int x) {
    vector<int> fl = factorList(x);
    if (fl.size() == 0)
      return {};
    vector<P> res(1, P(fl[0], 0));
    for (int p : fl) {
      if (res.back().first == p) {
        res.back().second++;
      } else {
        res.emplace_back(p, 1);
      }
    }
    return res;
  }
};
template <class t> t gcd(t a, t b) { return b != 0 ? gcd(b, a % b) : a; }
ll lcm(ll a, ll b) {
  ll g = gcd(a, b);
  return a / g * b;
}
bool prime(ll n) {
  for (ll i = 2; i <= sqrt(n); i++) {
    if (n % i == 0)
      return false;
  }
  return n != 1;
}
map<ll, ll> prime_factor(ll n) {
  map<ll, ll> ret;
  for (ll i = 2; i * i <= n; i++) {
    while (n % i == 0) {
      ret[i]++;
      n /= i;
    }
  }
  if (n != 1)
    ret[n] = 1;
  return ret;
}
ll modinv(ll a, ll m) {
  ll b = m, u = 1, v = 0;
  while (b) {
    ll t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= m;
  if (u < 0)
    u += m;
  return u;
}
vector<pair<char, int>> RunLength(string s) {
  if (s.size() == 0)
    return {};
  vector<pair<char, int>> res(1, pair<char, int>(s[0], 0));
  for (char p : s) {
    if (res.back().first == p) {
      res.back().second++;
    } else {
      res.emplace_back(p, 1);
    }
  }
  return res;
}
// Digit Count
int GetDigit(int num) { return log10(num) + 1; }
// bit calculation[how many "1"] (= __builtin_popcount())
int bit_count(int n) {
  int cnt = 0;
  while (n > 0) {
    if (n % 2 == 1)
      cnt++;
    n /= 2;
  }
  return cnt;
}
vector<long long> enum_divisors(long long N) {
  vector<long long> res;
  for (long long i = 1; i * i <= N; ++i) {
    if (N % i == 0) {
      res.push_back(i);
      if (N / i != i)
        res.push_back(N / i);
    }
  }
  sort(res.begin(), res.end());
  return res;
}
const ll dx[4] = {1, 0, -1, 0};
const ll dy[4] = {0, 1, 0, -1};
// struct edge { ll to, cost; };
typedef long double ld;
using Graph = vector<vector<int>>;
struct UnionFind {
  vector<ll> par; // 各元の親を表す配列
  vector<ll> siz; // 素集合のサイズを表す配列(1 で初期化)
  UnionFind() {}
  // Constructor
  UnionFind(ll sz_) : par(sz_), siz(sz_, 1) {
    for (ll i = 0; i < sz_; ++i)
      par[i] = i; // 初期では親は自分自身
  }
  void init(ll sz_) {
    par.resize(sz_);
    siz.resize(sz_, 1);
    for (ll i = 0; i < sz_; ++i)
      par[i] = i; // 初期では親は自分自身
  }

  // Member Function
  // Find
  ll root(ll x) { // 根の検索
    while (par[x] != x) {
      x = par[x] = par[par[x]]; // x の親の親を x の親とする
    }
    return x;
  }

  // Union(Unite, Merge)
  bool merge(ll x, ll y) {
    x = root(x);
    y = root(y);
    if (x == y)
      return false;
    // merge technique（データ構造をマージするテク．小を大にくっつける）
    if (siz[x] < siz[y])
      swap(x, y);
    siz[x] += siz[y];
    par[y] = x;
    return true;
  }

  bool issame(ll x, ll y) { // 連結判定
    return root(x) == root(y);
  }

  ll size(ll x) { // 素集合のサイズ
    return siz[root(x)];
  }
};
struct combination {
  vector<mint> fact, ifact;
  combination(int n) : fact(n + 1), ifact(n + 1) {
    // assert(n < mod);
    fact[0] = 1;
    for (int i = 1; i <= n; ++i)
      fact[i] = fact[i - 1] * i;
    ifact[n] = fact[n].inv();
    for (int i = n; i >= 1; --i)
      ifact[i - 1] = ifact[i] * i;
  }
  mint operator()(int n, int k) {
    if (k < 0 || k > n)
      return 0;
    return fact[n] * ifact[k] * ifact[n - k];
  }
};
struct edge {
  int to, cost;
};

/*
・MODあってる？？？
*/
int cnt[10000010];
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  // cout << fixed << setprecision(20);
  // combination com(2000010);
  int n;
  cin >> n;
  int ans = 0;
  for (int i = 1; i <= n; i++) {
    ans += i * (cnt[i] + 1);
    for (int j = 2 * i; j <= n; j += i)
      cnt[j]++;
  }
  cout << ans << endl;
  return 0;
}


Error: TLE

Fixed submission:

#include <algorithm>
#include <bitset>
#include <cassert>
#include <cfloat>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits.h>
#include <list>
#include <map>
#include <math.h>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
using namespace std;
#define int long long
#define ll long long
#define rep(i, n) for (ll i = 0; i < (n); i++)
#define P pair<ll, ll>
#define sz(x) (ll) x.size()
#define ALL(x) (x).begin(), (x).end()
#define ALLR(x) (x).rbegin(), (x).rend()
#define VE vector<ll>
#define COUT(x) cout << (x) << endl
#define MA map<ll, ll>
#define SE set<ll>
#define PQ priority_queue<ll>
#define PQR priority_queue<ll, VE, greater<ll>>
#define YES(n) cout << ((n) ? "YES" : "NO") << endl
#define Yes(n) cout << ((n) ? "Yes" : "No") << endl
#define EPS (1e-10)
#define pb push_back
long long MOD = 1000000007;
// long long MOD = 998244353;
const long long INF = 1LL << 60;
const long double PI = acos(-1.0);
struct mint {
  ll x; // typedef long long ll;
  mint(ll x = 0) : x((x % MOD + MOD) % MOD) {}
  mint operator-() const { return mint(-x); }
  mint &operator+=(const mint a) {
    if ((x += a.x) >= MOD)
      x -= MOD;
    return *this;
  }
  mint &operator-=(const mint a) {
    if ((x += MOD - a.x) >= MOD)
      x -= MOD;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= MOD;
    return *this;
  }
  mint operator+(const mint a) const {
    mint res(*this);
    return res += a;
  }
  mint operator-(const mint a) const {
    mint res(*this);
    return res -= a;
  }
  mint operator*(const mint a) const {
    mint res(*this);
    return res *= a;
  }
  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }
  // for prime MOD
  mint inv() const { return pow(MOD - 2); }
  mint &operator/=(const mint a) { return (*this) *= a.inv(); }
  mint operator/(const mint a) const {
    mint res(*this);
    return res /= a;
  }
  bool operator==(const mint a) const { return x == a.x; }
  bool operator!=(const mint a) const { return x != a.x; }
};
istream &operator>>(istream &is, const mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }
struct Sieve {
  int n;
  vector<int> f, primes;

  Sieve(int n = 1) : n(n), f(n + 1) {
    f[0] = f[1] = -1;
    for (ll i = 2; i <= n; ++i) {
      if (f[i])
        continue;
      primes.push_back(i);
      f[i] = i;
      for (ll j = i * i; j <= n; j += i) {
        if (!f[j])
          f[j] = i;
      }
    }
  }

  bool isPrime(int x) { return f[x] == x; }

  vector<int> factorList(int x) {
    vector<int> res;
    while (x != 1) {
      res.push_back(f[x]);
      x /= f[x];
    }
    return res;
  }

  vector<P> factor(int x) {
    vector<int> fl = factorList(x);
    if (fl.size() == 0)
      return {};
    vector<P> res(1, P(fl[0], 0));
    for (int p : fl) {
      if (res.back().first == p) {
        res.back().second++;
      } else {
        res.emplace_back(p, 1);
      }
    }
    return res;
  }
};
template <class t> t gcd(t a, t b) { return b != 0 ? gcd(b, a % b) : a; }
ll lcm(ll a, ll b) {
  ll g = gcd(a, b);
  return a / g * b;
}
bool prime(ll n) {
  for (ll i = 2; i <= sqrt(n); i++) {
    if (n % i == 0)
      return false;
  }
  return n != 1;
}
map<ll, ll> prime_factor(ll n) {
  map<ll, ll> ret;
  for (ll i = 2; i * i <= n; i++) {
    while (n % i == 0) {
      ret[i]++;
      n /= i;
    }
  }
  if (n != 1)
    ret[n] = 1;
  return ret;
}
ll modinv(ll a, ll m) {
  ll b = m, u = 1, v = 0;
  while (b) {
    ll t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= m;
  if (u < 0)
    u += m;
  return u;
}
vector<pair<char, int>> RunLength(string s) {
  if (s.size() == 0)
    return {};
  vector<pair<char, int>> res(1, pair<char, int>(s[0], 0));
  for (char p : s) {
    if (res.back().first == p) {
      res.back().second++;
    } else {
      res.emplace_back(p, 1);
    }
  }
  return res;
}
// Digit Count
int GetDigit(int num) { return log10(num) + 1; }
// bit calculation[how many "1"] (= __builtin_popcount())
int bit_count(int n) {
  int cnt = 0;
  while (n > 0) {
    if (n % 2 == 1)
      cnt++;
    n /= 2;
  }
  return cnt;
}
vector<long long> enum_divisors(long long N) {
  vector<long long> res;
  for (long long i = 1; i * i <= N; ++i) {
    if (N % i == 0) {
      res.push_back(i);
      if (N / i != i)
        res.push_back(N / i);
    }
  }
  sort(res.begin(), res.end());
  return res;
}
const ll dx[4] = {1, 0, -1, 0};
const ll dy[4] = {0, 1, 0, -1};
// struct edge { ll to, cost; };
typedef long double ld;
using Graph = vector<vector<int>>;
struct UnionFind {
  vector<ll> par; // 各元の親を表す配列
  vector<ll> siz; // 素集合のサイズを表す配列(1 で初期化)
  UnionFind() {}
  // Constructor
  UnionFind(ll sz_) : par(sz_), siz(sz_, 1) {
    for (ll i = 0; i < sz_; ++i)
      par[i] = i; // 初期では親は自分自身
  }
  void init(ll sz_) {
    par.resize(sz_);
    siz.resize(sz_, 1);
    for (ll i = 0; i < sz_; ++i)
      par[i] = i; // 初期では親は自分自身
  }

  // Member Function
  // Find
  ll root(ll x) { // 根の検索
    while (par[x] != x) {
      x = par[x] = par[par[x]]; // x の親の親を x の親とする
    }
    return x;
  }

  // Union(Unite, Merge)
  bool merge(ll x, ll y) {
    x = root(x);
    y = root(y);
    if (x == y)
      return false;
    // merge technique（データ構造をマージするテク．小を大にくっつける）
    if (siz[x] < siz[y])
      swap(x, y);
    siz[x] += siz[y];
    par[y] = x;
    return true;
  }

  bool issame(ll x, ll y) { // 連結判定
    return root(x) == root(y);
  }

  ll size(ll x) { // 素集合のサイズ
    return siz[root(x)];
  }
};
struct combination {
  vector<mint> fact, ifact;
  combination(int n) : fact(n + 1), ifact(n + 1) {
    // assert(n < mod);
    fact[0] = 1;
    for (int i = 1; i <= n; ++i)
      fact[i] = fact[i - 1] * i;
    ifact[n] = fact[n].inv();
    for (int i = n; i >= 1; --i)
      ifact[i - 1] = ifact[i] * i;
  }
  mint operator()(int n, int k) {
    if (k < 0 || k > n)
      return 0;
    return fact[n] * ifact[k] * ifact[n - k];
  }
};
struct edge {
  int to, cost;
};

/*
・MODあってる？？？
*/

map<int, map<int, int>> mp;
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  // cout << fixed << setprecision(20);
  // combination com(2000010);
  int n;
  cin >> n;
  int ans = 0;
  for (int i = 1; i <= n; i++) {
    if (i == 1) {
      ans += 1;
    } else {
      for (int j = 2;; j++) {
        if (i % j == 0) {
          mp[i] = mp[i / j];
          mp[i][j]++;
          break;
        }
      }
      int cnt = 1;
      for (auto p : mp[i]) {
        cnt *= p.second + 1;
      }
      ans += cnt * i;
    }
  }
  cout << ans << endl;
  return 0;
}