@article{Yang2024, 
author = {Shichun Yang and Qunying Liao and Shan Du and Huili Wang},
title = {The explicit formula and parity for some generalized Euler functions},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {5},
pages = {12458-12478},
keywords = {generalized Euler function, explicit formula, Möbius function, parity},
url = {https://www.sciopen.com/article/10.3934/math.2024609},
doi = {10.3934/math.2024609},
abstract = {Utilizing elementary methods and techniques, the explicit formula for the generalized Euler function        φ          e        (  n  )  (  e  =  8  ,  12  ) has been developed. Additionally, a sufficient and necessary condition for        φ          8        (  n  ) or        φ          12        (  n  ) to be odd has been obtained, respectively.}
}