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

#include <algorithm>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfloat>
#include <climits>
#include <cmath>
#include <cstdio>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_set>
#include <vector>
using namespace std;
typedef long double ld;
typedef long long int ll;
typedef unsigned long long int ull;
typedef vector<int> vi;
typedef vector<char> vc;
typedef vector<bool> vb;
typedef vector<double> vd;
typedef vector<string> vs;
typedef vector<ll> vll;
typedef vector<pair<int, int>> vpii;
typedef vector<pair<ll, ll>> vpll;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<vc> vvc;
typedef vector<vs> vvs;
typedef vector<vll> vvll;
typedef map<int, int> mii;
typedef set<int> si;
#define rep(i, n) for (ll i = 0; i < (n); ++i)
#define rrep(i, n) for (int i = 1; i <= (n); ++i)
#define arep(i, v) for (auto i : v)
#define irep(it, stl) for (auto it = stl.begin(); it != stl.end(); it++)
#define drep(i, n) for (int i = (n)-1; i >= 0; --i)
#define fin(ans) cout << (ans) << '\\n'
#define STLL(s) strtoll(s.c_str(), NULL, 10)
#define mp(p, q) make_pair(p, q)
#define pb(n) push_back(n)
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define Sort(a) sort(a.begin(), a.end())
#define Rort(a) sort(a.rbegin(), a.rend())
#define MATHPI acos(-1)
#define fi first
#define se second
constexpr int dx[8] = {1, 0, -1, 0, 1, -1, -1, 1};
constexpr int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1};
template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> inline void dump(T &v) {
  irep(i, v) { cout << *i << ((i == --v.end()) ? '\\n' : ' '); }
}
inline string getline() {
  string s;
  getline(cin, s);
  return s;
}
inline void yn(const bool b) { b ? fin("yes") : fin("no"); }
inline void Yn(const bool b) { b ? fin("Yes") : fin("No"); }
inline void YN(const bool b) { b ? fin("YES") : fin("NO"); }
struct io {
  io() {
    ios::sync_with_stdio(false);
    cin.tie(0);
  }
};
const int INF = INT_MAX;
constexpr ll LLINF = 1LL << 60;
constexpr ll MOD = 1000000007;
constexpr ld EPS = 1e-11;

constexpr int N = 10000001;
vector<int> num(N, 1);

int main() {

  int n;
  cin >> n;
  ll sum;
  ll ans = 0;
  for (int i = 2; i < N; i++) {
    for (int j = i; j < N; j += i) {
      num[j]++;
    }
  }
  for (ll i = 1; i <= n; i++) {
    ans += num[i] * i;
  }
  fin(ans);
}


Error: TLE

Fixed submission:

#include <algorithm>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfloat>
#include <climits>
#include <cmath>
#include <cstdio>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_set>
#include <vector>
using namespace std;
typedef long double ld;
typedef long long int ll;
typedef unsigned long long int ull;
typedef vector<int> vi;
typedef vector<char> vc;
typedef vector<bool> vb;
typedef vector<double> vd;
typedef vector<string> vs;
typedef vector<ll> vll;
typedef vector<pair<int, int>> vpii;
typedef vector<pair<ll, ll>> vpll;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<vc> vvc;
typedef vector<vs> vvs;
typedef vector<vll> vvll;
typedef map<int, int> mii;
typedef set<int> si;
#define rep(i, n) for (ll i = 0; i < (n); ++i)
#define rrep(i, n) for (int i = 1; i <= (n); ++i)
#define arep(i, v) for (auto i : v)
#define irep(it, stl) for (auto it = stl.begin(); it != stl.end(); it++)
#define drep(i, n) for (int i = (n)-1; i >= 0; --i)
#define fin(ans) cout << (ans) << '\\n'
#define STLL(s) strtoll(s.c_str(), NULL, 10)
#define mp(p, q) make_pair(p, q)
#define pb(n) push_back(n)
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define Sort(a) sort(a.begin(), a.end())
#define Rort(a) sort(a.rbegin(), a.rend())
#define MATHPI acos(-1)
#define fi first
#define se second
constexpr int dx[8] = {1, 0, -1, 0, 1, -1, -1, 1};
constexpr int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1};
template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> inline void dump(T &v) {
  irep(i, v) { cout << *i << ((i == --v.end()) ? '\\n' : ' '); }
}
inline string getline() {
  string s;
  getline(cin, s);
  return s;
}
inline void yn(const bool b) { b ? fin("yes") : fin("no"); }
inline void Yn(const bool b) { b ? fin("Yes") : fin("No"); }
inline void YN(const bool b) { b ? fin("YES") : fin("NO"); }
struct io {
  io() {
    ios::sync_with_stdio(false);
    cin.tie(0);
  }
};
const int INF = INT_MAX;
constexpr ll LLINF = 1LL << 60;
constexpr ll MOD = 1000000007;
constexpr ld EPS = 1e-11;

constexpr int N = 10000001;
vector<int> num(N, 1);
vector<map<int, int>> memo(N);
void eratosmake() {
  // 0と1を消す
  num[0] = num[1] = 1;
  for (int i = 2; i < N; i++) {
    if (num[i] == 1) {
      memo[i][i] = 1;
      for (int j = i << 1; j < N; j += i) {
        num[j] = i;
      }
    }
  }
}
void solve(int n) {
  if (n == 1) {
    memo[1][1] = 0;
  }
  if (memo[n].size() > 0)
    return;
  // if(memo[n/num[n]].size()==0){
  //     solve(n/num[n]);
  // }
  memo[n] = memo[n / num[n]];
  // if(memo[num[n]].size()==0){
  //     solve(num[n]);
  // }
  irep(i, memo[num[n]]) { memo[n][i->first] += i->second; }
}

int main() {

  eratosmake();
  int n;
  cin >> n;
  ll sum;
  ll ans = 0;
  for (int i = 1; i <= n; i++) {
    solve(i);
    sum = 1;
    irep(j, memo[i]) { sum *= (j->second + 1); }
    ans += sum * i;
  }
  fin(ans);
}