On Factorization as Bijection to Finite Sequences

We describe mechanisms to emulate multiplicative properties of prime numbers by connecting them to computationally simpler representations involving bijections from natural numbers to sequences and multisets of natural numbers. Through a generic framework, we model interesting properties of a canonical representation of factorization and its simpler equivalents. Among their shared properties, we study the information lost through factorization, we establish a connection to Catalan families. Keywords-sequence and multiset encodings and prime factorization, information loss through factorization, experimental mathematics and functional programming, declarative modeling of computational phenomena, factorization and Catalan families.