LCP
Counting recursive divisors
Number theory
Number of ordered factorizations and recursive divisors
Submitted (2024)
The number of recursive divisors and the number of ordered factorisations are two related arithmetic sequences that are recursively defined. But their recursive nature makes it hard to compute explicit values. We give three new closed-form expressions for these quantities, one of which is a generalised hypergeometric function. They shed light on the structure of these sequences and their number-theoretic properties.
Submitted (2024)