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  1. #include <iostream>
  2. #include <vector>
  3. #include <string>
  4. #include <algorithm>
  5. #include <cmath>
  6. #include <stdio.h>
  7. #include <string.h>
  8.  
  9. using namespace std;
  10. #define all(v) (v.begin()), (v.end())
  11.  
  12. void fast_io(){
  13.     ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
  14. }
  15.  
  16. int main()
  17. {
  18.     fast_io();
  19.     long long n=0;
  20.     cin >> n;
  21.     // prime factorization
  22.     long long factorSize = sqrt(n)+1;
  23.     long long factors[factorSize] = {0};
  24.     while (!(n%2)){
  25.         n /= 2;
  26.         factors[2]++;
  27.     }
  28.     for (int i = 3; i <= sqrt(n); i+=2){
  29.         if (n%i == 0){
  30.             n /= i;
  31.             factors[i]++;
  32.         }
  33.     }
  34.     factors[n]++;
  35.  
  36.     /* geometric sequence
  37.         - (2^0 + 2^1 + 2^2 + 2^3)
  38.         - An = (2)^(n-1)
  39.         - Sn = a(r^n - 1)/(r - 1)
  40.  
  41.     // the multiplication of the prime factor's gemetric squence is the formula
  42.     //∏k(∑i=0akpik)
  43.  
  44.     For example, the sum of all of the factors of 120=23⋅3⋅5 is
  45.         (1+2+22+23)(1+3)(1+5)=15⋅4⋅6=360
  46.     */
  47.  
  48.     long long sum = 1;
  49.  
  50.     for (int i = 0; i < factorSize; i++){
  51.         if (factors[i] == 0){continue;}
  52.         int n = factors[i]+1;
  53.         long long Sn = (pow(i, n) - 1)/(i-1);
  54.         sum *= Sn;
  55.     }
  56.     cout << sum << endl;
  57. }
Success #stdin #stdout 0s 5272KB
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https://ideone.com/0pjA1O
language:
C++ (gcc 8.3)
created:
7 days ago
visibility:
public

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