Recursive divisor properties
Properties of the recursive divisor function and the number of ordered factorisations
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.