Abstract: The aim of this paper is to conduct a survey on the average of some selected multiplicative arithmetic functions for large values of integers, while considering constraints imposed by the hereditary sum of digits function in base b, denoted by w_{b}. This investigation aims to provide insights into the behavior of these functions within the scope of the hereditary sum of digits.
Keywords: exponential sum; multiplicative arithmetic function; hereditary sum of digits function
DOI: DOI 10.14712/1213-7243.2026.008
AMS Subject Classification: 11A07 11A25 11A67 11L07 11N37 11N60 11N69