On the average value of the minimal Hamming multiple

TL;DR

This paper establishes an upper bound on the average minimal Hamming weight of multiples of positive integers and explores the solutions to equations involving this function, advancing understanding of its properties.

Contribution

It introduces a nontrivial upper bound on the average value of M(n) and provides new insights into the solutions of M(n)=M(n').

Findings

Derived a new upper bound on the average of M(n).

Identified conditions for solutions to M(n)=M(n').

Abstract

We find a nontrivial upper bound on the average value of the function M(n) which associates to every positive integer n the minimal Hamming weight of a multiple of n. Some new results about the equation M(n)=M(n') are given.