Arithmetic Functions For Modular Functions

The functions T (x) and S (x) are some arithmetic functions that have been given greater emphasis in the study of the divisors of a positive integer. With them we know what is the number of factors and the sum of them. The goal of this work is to extend those arithmetic functions to the theory of modular products or t_n - products. In this report, we analyzed the case for n = 0, 1, 2, 3, and 4. It is still in process, the case n = 5, for which is a more little complicate due to the amount of equivalences classes modulo 5. We also analyzed these functions in the case of comaximal products over Z. In addition to the definition we found some patterns that seems to be much closer to the Mersenne numbers. Still looking for results that can be obtained from the original theory of this arithmetic function.