Найти несократимые дроби

#include <iostream>
#include <numeric>
#include <vector>
 
void recursive_get_fractions(std::vector<std::pair<unsigned, unsigned>>&, unsigned, unsigned);
 
auto get_fractions(unsigned lim)
{
    std::vector<std::pair<unsigned, unsigned>> fractions;
    if (lim > 1) recursive_get_fractions(fractions, lim, lim - 1);
    return fractions;
}
 
void recursive_get_fractions(std::vector<std::pair<unsigned, unsigned>>& fractions, unsigned denominator, unsigned numerator)
{
    if (2 == denominator && 1 == numerator)
    {
        fractions.push_back(std::make_pair(numerator, denominator));
        return;
    }
    if (std::gcd(denominator, numerator) == 1)
    {
        fractions.push_back(std::make_pair(numerator, denominator));
        if (1 == numerator)
        {
            recursive_get_fractions(fractions, denominator - 1, denominator - 2);
            return;
        }
    }
    recursive_get_fractions(fractions, denominator, numerator - 1);
}
 
int main()
{
    std::cout << "Введите lim: ";
    unsigned lim;
    std::cin >> lim;
 
    auto fractions = get_fractions(lim);
 
    for (auto [num, denom] : fractions)
    {
        std::cout << num << "/" << denom << " ";
    }
 
    return 0;
}