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

/*
このコード、と～おれ!
Be accepted!
∧＿∧　
（｡･ω･｡)つ━☆・*。
⊂　　 ノ 　　　・゜+.
　しーＪ　　　°。+ *´¨)
 　　　　　　　　　.· ´¸.·*´¨) ¸.·*¨)
                  　　　　　　　　　　(¸.·´ (¸.·'* ☆
*/

#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstring>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <regex>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <vector>

////多倍長整数, cpp_intで宣言
// #include <boost/multiprecision/cpp_int.hpp>
// using namespace boost::multiprecision;

#pragma gcc target("avx2")
#pragma gcc optimization("Ofast")
#pragma gcc optimization("unroll-loops")
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define rep1(i, n) for (int i = 1; i <= (n); ++i)
#define rep2(i, n) for (int i = 2; i < (n); ++i)
#define repr(i, n) for (int i = n; i >= 0; --i)
#define reprm(i, n) for (int i = n - 1; i >= 0; --i)
#define printynl(a) printf(a ? "yes\\n" : "no\\n")
#define printyn(a) printf(a ? "Yes\\n" : "No\\n")
#define printYN(a) printf(a ? "YES\\n" : "NO\\n")
#define printim(a) printf(a ? "possible\\n" : "imposible\\n")
#define printdb(a) printf("%.50lf\\n", a)    // 少数出力
#define printLdb(a) printf("%.50Lf\\n", a)   // 少数出力
#define printdbd(a) printf("%.16lf\\n", a)   // 少数出力(桁少なめ)
#define prints(s) printf("%s\\n", s.c_str()) // string出力
#define all(x) (x).begin(), (x).end()
#define allsum(a, b, c) ((a + b) * c / 2LL) // 等差数列の和、初項,末項,項数
#define pb push_back
#define rpriq priq<int, vector<int>, greater<int>>
#define deg_to_rad(deg) (((deg) / 360.0L) * 2.0L * PI)
#define rad_to_deg(rad) (((rad) / 2.0L / PI) * 360.0L)
#define Please return
#define AC 0
#define manhattan_dist(a, b, c, d)                                             \\
  (abs(a - c) + abs(b - d)) /*(a, b) から (c, d) のマンハッタン距離 */
#define inf numeric_limits<double>::infinity();
#define linf numeric_limits<long double>::infinity()

using ll = long long;

constexpr int INF = 1073741823;
constexpr int MINF = -1073741823;
constexpr ll LINF = ll(4661686018427387903);
constexpr ll MOD = 1e9 + 7;
constexpr long double eps = 1e-6;
const long double PI = acosl(-1.0L);

using namespace std;

void scans(string &str) {
  char c;
  str = "";
  scanf("%c", &c);
  if (c == '\\n')
    scanf("%c", &c);
  while (c != '\\n' && c != -1 && c != ' ') {
    str += c;
    scanf("%c", &c);
  }
}

void scanc(char &str) {
  char c;
  scanf("%c", &c);
  if (c == -1)
    return;
  while (c == '\\n') {
    scanf("%c", &c);
  }
  str = c;
}

double acot(double x) { return PI / 2 - atan(x); }

ll LSB(ll n) { return (n & (-n)); }

/*-----------------------------------------ここからコード-----------------------------------------*/

const int MAX = 15001000;
bool IsPrime[MAX];
int MinFactor[MAX];

vector<int> preprocess(int n = MAX) {
  vector<int> res;
  for (int i = 0; i < n; ++i)
    IsPrime[i] = true, MinFactor[i] = -1;
  IsPrime[0] = false;
  IsPrime[1] = false;
  MinFactor[0] = 0;
  MinFactor[1] = 1;
  for (int i = 2; i < n; ++i) {
    if (IsPrime[i]) {
      MinFactor[i] = i;
      res.push_back(i);
      for (int j = i * 2; j < n; j += i) {
        IsPrime[j] = false;
        if (MinFactor[j] == -1)
          MinFactor[j] = i;
      }
    }
  }
  return res;
}

vector<pair<int, int>> prime_factor(int n) {
  vector<pair<int, int>> res;
  while (n != 1) {
    int prime = MinFactor[n];
    int exp = 0;
    while (MinFactor[n] == prime) {
      ++exp;
      n /= prime;
    }
    res.push_back(make_pair(prime, exp));
  }
  return res;
}

int main() {

  ll n, ans = 0;
  scanf("%lld", &n);
  preprocess();
  rep(i, n) {
    auto f = prime_factor(i + 1);
    ll tmp = 1;
    for (const auto &[a, b] : f)
      tmp *= b + 1;
    ans += tmp * (ll)(i + 1);
  }
  printf("%lld\\n", ans);

  Please AC;
}

Error: TLE

Fixed submission:

/*
このコード、と～おれ!
Be accepted!
∧＿∧　
（｡･ω･｡)つ━☆・*。
⊂　　 ノ 　　　・゜+.
　しーＪ　　　°。+ *´¨)
 　　　　　　　　　.· ´¸.·*´¨) ¸.·*¨)
                  　　　　　　　　　　(¸.·´ (¸.·'* ☆
*/

#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstring>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <regex>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <vector>

////多倍長整数, cpp_intで宣言
// #include <boost/multiprecision/cpp_int.hpp>
// using namespace boost::multiprecision;

#pragma gcc target("avx2")
#pragma gcc optimization("Ofast")
#pragma gcc optimization("unroll-loops")
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define rep1(i, n) for (int i = 1; i <= (n); ++i)
#define rep2(i, n) for (int i = 2; i < (n); ++i)
#define repr(i, n) for (int i = n; i >= 0; --i)
#define reprm(i, n) for (int i = n - 1; i >= 0; --i)
#define printynl(a) printf(a ? "yes\\n" : "no\\n")
#define printyn(a) printf(a ? "Yes\\n" : "No\\n")
#define printYN(a) printf(a ? "YES\\n" : "NO\\n")
#define printim(a) printf(a ? "possible\\n" : "imposible\\n")
#define printdb(a) printf("%.50lf\\n", a)    // 少数出力
#define printLdb(a) printf("%.50Lf\\n", a)   // 少数出力
#define printdbd(a) printf("%.16lf\\n", a)   // 少数出力(桁少なめ)
#define prints(s) printf("%s\\n", s.c_str()) // string出力
#define all(x) (x).begin(), (x).end()
#define allsum(a, b, c) ((a + b) * c / 2LL) // 等差数列の和、初項,末項,項数
#define pb push_back
#define rpriq priq<int, vector<int>, greater<int>>
#define deg_to_rad(deg) (((deg) / 360.0L) * 2.0L * PI)
#define rad_to_deg(rad) (((rad) / 2.0L / PI) * 360.0L)
#define Please return
#define AC 0
#define manhattan_dist(a, b, c, d)                                             \\
  (abs(a - c) + abs(b - d)) /*(a, b) から (c, d) のマンハッタン距離 */
#define inf numeric_limits<double>::infinity();
#define linf numeric_limits<long double>::infinity()

using ll = long long;

constexpr int INF = 1073741823;
constexpr int MINF = -1073741823;
constexpr ll LINF = ll(4661686018427387903);
constexpr ll MOD = 1e9 + 7;
constexpr long double eps = 1e-6;
const long double PI = acosl(-1.0L);

using namespace std;

void scans(string &str) {
  char c;
  str = "";
  scanf("%c", &c);
  if (c == '\\n')
    scanf("%c", &c);
  while (c != '\\n' && c != -1 && c != ' ') {
    str += c;
    scanf("%c", &c);
  }
}

void scanc(char &str) {
  char c;
  scanf("%c", &c);
  if (c == -1)
    return;
  while (c == '\\n') {
    scanf("%c", &c);
  }
  str = c;
}

double acot(double x) { return PI / 2 - atan(x); }

ll LSB(ll n) { return (n & (-n)); }

/*-----------------------------------------ここからコード-----------------------------------------*/

map<int64_t, int> prime_factor(int64_t n) {
  map<int64_t, int> ret;
  for (int64_t i = 2; i * i <= n; i++) {
    while (n % i == 0) {
      ret[i]++;
      n /= i;
    }
  }
  if (n != 1)
    ret[n] = 1;
  return ret;
}

int main() {

  ll n, ans = 0;
  scanf("%lld", &n);
  rep(i, n) {
    ll tmp = 1;
    for (const auto &aa : prime_factor(i + 1))
      tmp *= aa.second + 1;
    ans += tmp * (ll)(i + 1);
  }
  printf("%lld\\n", ans);

  Please AC;
}