A Central Limit Theorem for the Number of Distinct Degrees of Prime Factors in Additive Arithmetical Semigroups

In this paper, we will prove a central limit theorem for the number of distinct degrees of prime factors of elements of additive arithmetical semigroups. Besides information on the distribution of distinct degrees of prime factors, this provides an interesting natural example of a central limit theorem for a non-additive function in an additive arithmetical semigroup.