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

// include
//------------------------------------------
#include <bits/stdc++.h>
using namespace std;

// typedef
//------------------------------------------
using LL = int64_t;
using VL = vector<LL>;
using VVL = vector<VL>;
using VS = vector<string>;
using PLL = pair<LL, LL>;

// container util
//------------------------------------------
#define whole(f, x, ...)                                                       \\
  ([&](decltype((x)) whole) {                                                  \\
    return (f)(begin(whole), end(whole), ##__VA_ARGS__);                       \\
  })(x)
#define rwhole(f, x, ...)                                                      \\
  ([&](decltype((x)) whole) {                                                  \\
    return (f)(rbegin(whole), rend(whole), ##__VA_ARGS__);                     \\
  })(x)
#define EACH(i, c)                                                             \\
  for (decltype((c).begin()) i = (c).begin(); i != (c).end(); ++i)
#define EXIST(s, e) ((s).find(e) != (s).end())
#define ALL(x) ::std::begin(x), ::std::end(x)
#define RALL(x) ::std::rbegin(x), ::std::rend(x)
#define SORT(c) whole(sort, c)
#define RSORT(c) rwhole(sort, c)

// constant
//--------------------------------------------
constexpr double EPS = 1e-10;
constexpr double PI = 3.14159265358979323846;
constexpr int MOD = 1000000007;

// grid
//--------------------------------------------
VL dx = {0, 1, 0, -1};
VL dy = {1, 0, -1, 0};
VL dx2 = {-1, 0, 1, -1, 1, -1, 0, 1};
VL dy2 = {-1, -1, -1, 0, 0, 1, 1, 1};

// debug
//--------------------------------------------
#define dump(x) cerr << #x << " = " << (x) << endl;
#define debug(x)                                                               \\
  cerr << #x << " = " << (x) << " (L" << __LINE__ << ")"                       \\
       << " " << __FILE__ << endl;

// IO accelerate
//--------------------------------------------
struct InitIO {
  InitIO() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(30);
  }
} init_io;

// template
//--------------------------------------------
//  declaretion
template <typename T> istream &operator>>(istream &is, vector<T> &vec);
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p);
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec);
template <typename T>
ostream &operator<<(ostream &os, const vector<vector<T>> &vv);
template <typename T> vector<T> make_v(size_t a);
template <typename T, typename... Ts> auto make_v(size_t a, Ts... ts);
template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v);
template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v);

// implementation
template <typename T> istream &operator>>(istream &is, vector<T> &vec) {
  for (T &x : vec)
    is >> x;
  return is;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << "," << p.second;
  return os;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) {
  for (int i = 0; i < vec.size(); i++) {
    os << vec[i] << (i + 1 == vec.size() ? "" : "\\t");
  }
  return os;
}
template <typename T>
ostream &operator<<(ostream &s, const vector<vector<T>> &vv) {
  for (int i = 0; i < vv.size(); ++i) {
    s << vv[i] << endl;
  }
  return s;
}

// 多重vector
// auto dp=make_v<int>(4,h,w) みたいに使える
template <typename T> vector<T> make_v(size_t a) { return vector<T>(a); }

template <typename T, typename... Ts> auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

// 多重vectorのためのfill
// fill_v(dp,0) みたいに使える
template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
  for (auto &e : t)
    fill_v(e, v);
}

template <class T, class U> void chmax(T &a, U b) {
  if (a < b)
    a = b;
}
template <class T, class U> void chmin(T &a, U b) {
  if (b < a)
    a = b;
}
template <typename T> T gcd(T a, T b) { return b ? gcd(b, a % b) : a; }
template <typename T> T lcm(T a, T b) { return a / gcd(a, b) * b; }

// main code

VL primeList(LL num) {
  VL ret;
  vector<bool> is_prime(num + 1, true);
  for (LL i = 2; i <= (LL)sqrt(num) + 1; i++) {
    if (is_prime[i]) {
      for (int j = i * 2; j <= num; j += i) {
        is_prime[j] = false;
      }
    }
  }
  for (int i = 2; i <= num; i++) {
    if (is_prime[i]) {
      ret.push_back(i);
    }
  }
  return ret;
}

int main(int argc, char *argv[]) {
  LL n;
  cin >> n;
  auto pl = primeList(n);
  LL ans = 0;
  VL kosuu(n + 1, 1);
  for (auto i : pl) {
    kosuu[i] = 2;
    for (int j = i + i; j <= n; j += i) {
      LL tmp = 1;
      LL tmpj = j;
      while (tmpj % i == 0) {
        tmp++;
        tmpj /= i;
      }
      kosuu[j] *= tmp;
    }
  }
  for (LL i = 1; i < n + 1; i++) {
    ans += i * kosuu[i];
  }
  cout << ans << endl;
  return 0;
}

Error: TLE

Fixed submission:

// include
//------------------------------------------
#include <bits/stdc++.h>
using namespace std;

// typedef
//------------------------------------------
using LL = int64_t;
using VL = vector<LL>;
using VVL = vector<VL>;
using VS = vector<string>;
using PLL = pair<LL, LL>;

// container util
//------------------------------------------
#define whole(f, x, ...)                                                       \\
  ([&](decltype((x)) whole) {                                                  \\
    return (f)(begin(whole), end(whole), ##__VA_ARGS__);                       \\
  })(x)
#define rwhole(f, x, ...)                                                      \\
  ([&](decltype((x)) whole) {                                                  \\
    return (f)(rbegin(whole), rend(whole), ##__VA_ARGS__);                     \\
  })(x)
#define EACH(i, c)                                                             \\
  for (decltype((c).begin()) i = (c).begin(); i != (c).end(); ++i)
#define EXIST(s, e) ((s).find(e) != (s).end())
#define ALL(x) ::std::begin(x), ::std::end(x)
#define RALL(x) ::std::rbegin(x), ::std::rend(x)
#define SORT(c) whole(sort, c)
#define RSORT(c) rwhole(sort, c)

// constant
//--------------------------------------------
constexpr double EPS = 1e-10;
constexpr double PI = 3.14159265358979323846;
constexpr int MOD = 1000000007;

// grid
//--------------------------------------------
VL dx = {0, 1, 0, -1};
VL dy = {1, 0, -1, 0};
VL dx2 = {-1, 0, 1, -1, 1, -1, 0, 1};
VL dy2 = {-1, -1, -1, 0, 0, 1, 1, 1};

// debug
//--------------------------------------------
#define dump(x) cerr << #x << " = " << (x) << endl;
#define debug(x)                                                               \\
  cerr << #x << " = " << (x) << " (L" << __LINE__ << ")"                       \\
       << " " << __FILE__ << endl;

// IO accelerate
//--------------------------------------------
struct InitIO {
  InitIO() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(30);
  }
} init_io;

// template
//--------------------------------------------
//  declaretion
template <typename T> istream &operator>>(istream &is, vector<T> &vec);
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p);
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec);
template <typename T>
ostream &operator<<(ostream &os, const vector<vector<T>> &vv);
template <typename T> vector<T> make_v(size_t a);
template <typename T, typename... Ts> auto make_v(size_t a, Ts... ts);
template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v);
template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v);

// implementation
template <typename T> istream &operator>>(istream &is, vector<T> &vec) {
  for (T &x : vec)
    is >> x;
  return is;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << "," << p.second;
  return os;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) {
  for (int i = 0; i < vec.size(); i++) {
    os << vec[i] << (i + 1 == vec.size() ? "" : "\\t");
  }
  return os;
}
template <typename T>
ostream &operator<<(ostream &s, const vector<vector<T>> &vv) {
  for (int i = 0; i < vv.size(); ++i) {
    s << vv[i] << endl;
  }
  return s;
}

// 多重vector
// auto dp=make_v<int>(4,h,w) みたいに使える
template <typename T> vector<T> make_v(size_t a) { return vector<T>(a); }

template <typename T, typename... Ts> auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

// 多重vectorのためのfill
// fill_v(dp,0) みたいに使える
template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
  for (auto &e : t)
    fill_v(e, v);
}

template <class T, class U> void chmax(T &a, U b) {
  if (a < b)
    a = b;
}
template <class T, class U> void chmin(T &a, U b) {
  if (b < a)
    a = b;
}
template <typename T> T gcd(T a, T b) { return b ? gcd(b, a % b) : a; }
template <typename T> T lcm(T a, T b) { return a / gcd(a, b) * b; }

// main code

VL primeList(LL num) {
  VL ret;
  vector<bool> is_prime(num + 1, true);
  for (LL i = 2; i <= (LL)sqrt(num) + 1; i++) {
    if (is_prime[i]) {
      for (int j = i * 2; j <= num; j += i) {
        is_prime[j] = false;
      }
    }
  }
  for (int i = 2; i <= num; i++) {
    if (is_prime[i]) {
      ret.push_back(i);
    }
  }
  return ret;
}

int main(int argc, char *argv[]) {
  LL n;
  cin >> n;
  auto pl = primeList(n);
  LL ans = 1;
  // vector<bool> is_prime(n+1,false);
  // for (auto i : pl) {
  //	is_prime[i] = true;
  // }
  vector<map<int, int>> memo(n + 1);
  for (LL i = 2; i <= n; i++) {
    // if (is_prime[i]) {
    if (binary_search(ALL(pl), i)) {
      ans += i * 2;
      memo[i][i]++;
    } else {
      for (LL j = 0; j < pl.size(); j++) {
        if (i % pl[j] == 0) {
          map<int, int> mp = memo[i / pl[j]];
          mp[pl[j]]++;
          memo[i] = mp;
          LL tmp = 1;
          for (auto [key, val] : mp) {
            tmp *= (LL)val + 1;
          }
          ans += tmp * i;
          break;
        }
      }
    }
  }
  // dump(memo);
  cout << ans << endl;
  return 0;
}