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#include <iostream>
#include <type_traits>
 
// List of factors
template<std::intmax_t ... Misc> 
struct factors { };
 
// Declaration
template<std::intmax_t ... Misc> 
struct factorization;
 
// Initial specialization
template<std::intmax_t Value> 
struct factorization<Value>
{
    typedef typename std::conditional<Value % 2 == 0,
            typename factorization<Value / 2, 2, 2>::type,
            typename factorization<Value / 2, 2 + 1>::type>::type type;
};
 
// Initial specialization when the value is not divisible by 2
template<std::intmax_t Value, std::intmax_t Divisor> 
struct factorization<Value, Divisor>
{
    typedef typename std::conditional<Value % Divisor == 0,
            typename factorization<Value / Divisor, Divisor, Divisor>::type,
            typename factorization<Value / Divisor, Divisor + 1>::type>::type type;
};
 
// Specialization after the first recusion step
template<std::intmax_t Value, std::intmax_t Divisor, std::intmax_t Prime> 
struct factorization<Value, Divisor, Prime>
{
    typedef typename std::conditional<Value % Divisor == 0,
            typename factorization<Value / Divisor, Divisor, Divisor>::type,
            typename factorization<Value / Divisor, Divisor + 1>::type>::type type;
};
 
// Recursion specialization
template<std::intmax_t Value, std::intmax_t Divisor, std::intmax_t Prime, std::intmax_t ... Primes> 
struct factorization<Value, Divisor, Prime, Primes...>
{
    typedef typename std::conditional<Value % Divisor == 0 && Divisor != Prime,
            typename factorization<Value / Divisor, Divisor, Divisor, Prime,
                    Primes...>::type,
            typename factorization<
                    Value % Divisor == 0 ? Value / Divisor : Value,
                    Divisor + (Value % Divisor != 0), Prime, Primes...>::type>::type type;
};
 
// Last recursion step
template<std::intmax_t Value, std::intmax_t ... Primes> 
struct factorization<Value, Value, Primes...>
{
    typedef typename factorization<1, Value, Value, Primes...>::type type;
};
 
// Finalize
template<std::intmax_t Divisor, std::intmax_t ... Primes> 
struct factorization<1, Divisor, Primes...>
{
    typedef factors<Primes...> type;
};
 
// Main
int main() {
	typename factorization<18>::type x;
	return 0;
}

prog.cpp: In instantiation of ‘struct factorization<4ll, 2ll, 2ll>’:
prog.cpp:36:79:   required from ‘struct factorization<9ll, 2ll, 2ll>’
prog.cpp:18:67:   required from ‘struct factorization<18ll>’
prog.cpp:67:28:   required from here
prog.cpp:36:79: error: ambiguous class template instantiation for ‘struct factorization<2ll, 2ll, 2ll>’
             typename factorization<Value / Divisor, Divisor + 1>::type>::type type;
                                                                               ^
prog.cpp:32:8: error: candidates are: struct factorization<Value, Divisor, Prime>
 struct factorization<Value, Divisor, Prime>
        ^
prog.cpp:41:8: error:                 struct factorization<Value, Divisor, Prime, Primes ...>
 struct factorization<Value, Divisor, Prime, Primes...>
        ^
prog.cpp:53:8: error:                 struct factorization<Value, Value, Primes ...>
 struct factorization<Value, Value, Primes...>
        ^
prog.cpp:36:79: error: invalid use of incomplete type ‘struct factorization<2ll, 2ll, 2ll>’
             typename factorization<Value / Divisor, Divisor + 1>::type>::type type;
                                                                               ^
prog.cpp:10:8: error: declaration of ‘struct factorization<2ll, 2ll, 2ll>’
 struct factorization;
        ^
prog.cpp: In function ‘int main()’:
prog.cpp:67:30: error: invalid combination of multiple type-specifiers
  typename factorization<18>::type x;
                              ^
prog.cpp:67:36: error: invalid type in declaration before ‘;’ token
  typename factorization<18>::type x;
                                    ^
prog.cpp:67:35: warning: unused variable ‘x’ [-Wunused-variable]
  typename factorization<18>::type x;
                                   ^

Standard output is empty