Exponential divisor functions
Author:


2010 Mathematics Subject Classification:

11N37, 11M06, 11A25.

Keywords:

average order, exponential divisor function, generalized divisor function.

Abstract:

We consider the operator on arithmetic functions such that is the multiplicative arithmetic function defined by for every prime power . We investigate the behaviour of , where is a dimensional divisor function and stands for the fold iterate of . We estimate the error terms of for various combinations of and . We also study properties of for arbitrary and sufficiently large . We improve special cases of the Dirichlet asymmetric divisor problem and several results on the exponential divisor and totient functions, also.

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Vol. 10 (18), 2015
