Recursive divisor properties
The recursive divisor function is found to have a simple generating function, which leads to a number of new Dirichlet convolutions.
Properties of the recursive divisor function
We recently introduced a new arithmetic function called the recursive divisor function, . Here we show that its Dirichlet series is , where is the Riemann-zeta function. We relate the recursive divisor function to the ordinary divisor function, , which yields a number of new Dirichlet convolutions. We also state the equivalent of the Riemann hypothesis in terms of .