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

//                _
//  ___ _ __ ___ (_) __ ___      ___   _ _ __ ___  _ __
// / __| '_ ` _ \\| |/ _` \\ \\ /\\ / / | | | '_ ` _ \\| '_ \\ 
// \\__ \\ | | | | | | (_| |\\ V  V /| |_| | | | | | | |_) |
// |___/_| |_| |_|_|\\__, | \\_/\\_/  \\__,_|_| |_| |_| .__/
//                  |___/                         |_|
// code by smigwump
// https://codeforces.com/blog/entry/62393
#include <bits/stdc++.h>
#define PB push_back
#define MP make_pair
#define F first
#define S second
typedef long long ll;
#define REP(i, a, b) for (ll i = a; i <= b; i++)
#define PER(i, a, b) for (ll i = a; i >= b; i--)

using namespace std;

int main() {
  // #ifndef ONLINE_JUDGE
  //     freopen("input.txt", "r", stdin);
  //     freopen("output.txt", "w", stdout);
  // #endif

  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  ll n;
  cin >> n;
  ll ans = 0;
  REP(i, 1, n) {
    ll temp = n / i;
    ans += (i * temp * (temp + 1)) / 2;
  }

  cout << ans << "\\n";
  return 0;
}


Error: TLE

Fixed submission:

//                _
//  ___ _ __ ___ (_) __ ___      ___   _ _ __ ___  _ __
// / __| '_ ` _ \\| |/ _` \\ \\ /\\ / / | | | '_ ` _ \\| '_ \\ 
// \\__ \\ | | | | | | (_| |\\ V  V /| |_| | | | | | | |_) |
// |___/_| |_| |_|_|\\__, | \\_/\\_/  \\__,_|_| |_| |_| .__/
//                  |___/                         |_|
// code by smigwump
// https://codeforces.com/blog/entry/62393
#include <bits/stdc++.h>
#define PB push_back
#define MP make_pair
#define F first
#define S second
typedef long long ll;
#define REP(i, a, b) for (ll i = a; i <= b; i++)
#define PER(i, a, b) for (ll i = a; i >= b; i--)

using namespace std;
// ll countDivisors(ll n)
// {
// 	ll cnt = 0;
// 	for (ll i = 1; i <= sqrt(n); i++) {
// 		if (n % i == 0) {
// 			if (n / i == i)
// 				cnt++;

// 			else
// 				cnt = cnt + 2;
// 		}
// 	}
// 	return cnt;
// }
void SieveOfEratosthenes(int n, bool prime[], bool primesquare[], int a[]) {
  // Create a boolean array "prime[0..n]" and
  // initialize all entries it as true. A value
  // in prime[i] will finally be false if i is
  // Not a prime, else true.
  for (int i = 2; i <= n; i++)
    prime[i] = true;

  // Create a boolean array "primesquare[0..n*n+1]"
  // and initialize all entries it as false. A value
  // in squareprime[i] will finally be true if i is
  // square of prime, else false.
  for (int i = 0; i <= (n * n + 1); i++)
    primesquare[i] = false;

  // 1 is not a prime number
  prime[1] = false;

  for (int p = 2; p * p <= n; p++) {
    // If prime[p] is not changed, then
    // it is a prime
    if (prime[p] == true) {
      // Update all multiples of p
      for (int i = p * 2; i <= n; i += p)
        prime[i] = false;
    }
  }

  int j = 0;
  for (int p = 2; p <= n; p++) {
    if (prime[p]) {
      // Storing primes in an array
      a[j] = p;

      // Update value in primesquare[p*p],
      // if p is prime.
      primesquare[p * p] = true;
      j++;
    }
  }
}

// Function to count divisors
int countDivisors(int n) {
  // If number is 1, then it will have only 1
  // as a factor. So, total factors will be 1.
  if (n == 1)
    return 1;

  bool prime[n + 1], primesquare[n * n + 1];

  int a[n]; // for storing primes upto n

  // Calling SieveOfEratosthenes to store prime
  // factors of n and to store square of prime
  // factors of n
  SieveOfEratosthenes(n, prime, primesquare, a);

  // ans will contain total number of distinct
  // divisors
  int ans = 1;

  // Loop for counting factors of n
  for (int i = 0;; i++) {
    // a[i] is not less than cube root n
    if (a[i] * a[i] * a[i] > n)
      break;

    // Calculating power of a[i] in n.
    int cnt = 1;          // cnt is power of prime a[i] in n.
    while (n % a[i] == 0) // if a[i] is a factor of n
    {
      n = n / a[i];
      cnt = cnt + 1; // incrementing power
    }

    // Calculating number of divisors
    // If n = a^p * b^q then total divisors of n
    // are (p+1)*(q+1)
    ans = ans * cnt;
  }

  // if a[i] is greater than cube root of n

  // First case
  if (prime[n])
    ans = ans * 2;

  // Second case
  else if (primesquare[n])
    ans = ans * 3;

  // Third casse
  else if (n != 1)
    ans = ans * 4;

  return ans; // Total divisors
}

int main() {
  // #ifndef ONLINE_JUDGE
  //     freopen("input.txt", "r", stdin);
  //     freopen("output.txt", "w", stdout);
  // #endif

  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  ll n;
  cin >> n;
  ll ans = 0;
  vector<ll> v(n + 1, 0);
  v[1] = 1;
  REP(i, 2, n) { v[i] = countDivisors(i); }
  // for(auto it:v) {
  // 	cout<<it<<"\\n";
  // }
  // cout<<"bruhmex\\n";
  REP(i, 1, n) { ans += (i * v[i]); }
  cout << ans << "\\n";
  // cout<<countDivisors(12)<<"\\n";
  return 0;
}