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math.NT2023
Number of ordered factorizations and recursive divisors
T. M. A. Fink
The number of ordered factorizations and the number of recursive divisors are two related arithmetic functions that are recursively defined. But it is hard to construct explicit re…
math.NT2023
Properties of the recursive divisor function and the number of ordered factorizations
T. M. A. Fink
We recently introduced the recursive divisor function , a recursive analogue of the usual divisor function. Here we calculate its Dirichlet series, which is ${ζ(s-x)}/(2 -…