Une remarque sur l'arborification de Matula

TL;DR

This paper proposes applying Matula's arborification technique to analyze the partial sums of the Möbius and Liouville functions, offering a new perspective on their behavior in number theory.

Contribution

It introduces a novel application of Matula's arborification to the study of summatory functions of Möbius and Liouville functions, bridging combinatorial methods with number theory.

Findings

Potential new insights into the behavior of Möbius and Liouville sums

Application of arborification to number-theoretic functions

Framework for further analytical exploration

Abstract

Nous esquissons une application de l'arborification de Matula \`a l'\'etude de la fonction sommatoire des fonctions de M\" obius et de Liouville sur les entiers naturels - We sketch an application of Matula's arborification to the study of the partial sums of both M\" obius and Liouville function.