Menon-type identities concerning subsets of the set $\{1,2,\ldots,n\}$

TL;DR

This paper establishes Menon-type identities involving subsets of the set {1, 2, ..., n} and functions studied by Nathanson, expanding the understanding of these identities in combinatorial number theory.

Contribution

The paper introduces new Menon-type identities related to subsets of finite sets and specific arithmetic functions, extending Nathanson's previous work.

Findings

Proved identities linking subsets and arithmetic functions

Extended Nathanson's functions with new combinatorial identities

Enhanced understanding of Menon-type identities in subset contexts

Abstract

We prove certain Menon-type identities associated with the subsets of the set $\{1,2,\ldots,n\}$ and related to the functions $f$, $f_k$, $\Phi$ and $\Phi_k$, defined and investigated by Nathanson (2007).