Image for the paper "Properties of the recursive divisor function and the number of ordered factorisations"
Image for the paper "Properties of the recursive divisor function and the number of ordered factorisations"
Image for the paper "Properties of the recursive divisor function and the number of ordered factorisations"
Image for the paper "Properties of the recursive divisor function and the number of ordered factorisations"
LCP
Image for the paper "Properties of the recursive divisor function and the number of ordered factorisations"
Image for the paper "Properties of the recursive divisor function and the number of ordered factorisations"
Image for the paper "Properties of the recursive divisor function and the number of ordered factorisations"
Image for the paper "Properties of the recursive divisor function and the number of ordered factorisations"
Image for the paper "Properties of the recursive divisor function and the number of ordered factorisations"
Image for the paper "Properties of the recursive divisor function and the number of ordered factorisations"
Image for the paper "Properties of the recursive divisor function and the number of ordered factorisations"
Image for the paper "Properties of the recursive divisor function and the number of ordered factorisations"
Image for the paper "Properties of the recursive divisor function and the number of ordered factorisations"
Image for the paper "Properties of the recursive divisor function and the number of ordered factorisations"
Image for the paper "Properties of the recursive divisor function and the number of ordered factorisations"
Image for the paper "Properties of the recursive divisor function and the number of ordered factorisations"

Recursive divisor properties

Number theory

Properties of the recursive divisor function and the number of ordered factorisations

Arxiv (2023)

T. Fink

We recently introduced the recursive divisor function κx(n)\kappa_x(n). Here we calculate its Dirichlet series, which is ζ(sx)/(2ζ(s)){\zeta(s-x)}/(2 - \zeta(s)). We show that κx(n)\kappa_x(n) is related to the ordinary divisor function by κxσy=κyσx\kappa_x * \sigma_y = \kappa_y * \sigma_x, where * denotes the Dirichlet convolution. Using this, we derive several relations between κx(n)\kappa_x(n) and standard arithmetic functions, and clarify the relation between κ0(n)\kappa_0(n) and the number of ordered factorisations.

Arxiv (2023)

T. Fink