Recursive divisor properties
Number theory
Properties of the recursive divisor function and the number of ordered factorisations
Arxiv for Proceedings of the American Mathematical Society (2023)
We recently introduced the recursive divisor function . Here we calculate its Dirichlet series, which is . We show that is related to the ordinary divisor function by , where * denotes the Dirichlet convolution. Using this, we derive several relations between and standard arithmetic functions, and clarify the relation between and the number of ordered factorisations.
Arxiv for Proceedings of the American Mathematical Society (2023)