To answer this problem correctly, find \(S_i\) for each \(i = 0, 1, 2, \ldots, N\) just as instructed in the problem statement to construct the sought string \(s_0s_1\ldots s_N\).

One can perform an operation for each \(i = 0, 1, 2, \ldots, N\), and inspect each integer between \(1\) and \(9\) as a candidate of \(j\), with a loop feature (like a for statement) which is a standard feature of a programming language.

The following is a sample code in C++ language.

#include <iostream>
using namespace std;

int main(void)
{
  int n;
  cin >> n;
  
  string s;
  for(int i = 0; i <= n; i++){
    s += "-";
    for(int j = 1; j <= 9; j++){
      if(n % j == 0 && i % (n/j) == 0){
        s[i] = j + '0';
        break;
      }
    }
  }
  cout << s << endl;
  
  return 0;
}