An analog of the arithmetic triangle obtained by replacing the products by the least common multiples

TL;DR

This paper introduces a new arithmetic triangle by replacing binomial coefficient products with least common multiples, exploring its properties and posing open questions about its structure.

Contribution

It presents a novel analog of the arithmetic triangle using least common multiples instead of products, expanding combinatorial and number-theoretic understanding.

Findings

Defined the new arithmetic triangle with LCM-based entries

Established initial properties of the triangle

Posed open questions for further research

Abstract

In this paper, we introduce an analog of the Al-Karaji arithmetic triangle by substituting in the formula of the binomial coefficients the products by the least common multiples. Then, we give some properties and some open questions related to the obtained triangle.