Ordered Atomic Factorization

There has been a number of papers that point out that it is possible to make ordered factorizations, but there is very little literature about it. We pretend to identify the number of ordered atomic factorizations of a number $N$, we named these factorizations tau less equal factorizations. We denote Pⁿ a prime number to the n^th power and c(N) the number of tau less equal factorizations of an arbitrary natural number N. We can performed a method to count the number of the factorizations, because the order enables a way of arranging the factorization in such a way that it is simpler to count. The significance of the research is that it was possible to get the number of these ordered factorizations by simply calculating the determinant of a matrix that applies to every single case of factorization.