On the largest prime factors of consecutive square-free integers

Puntos clave

• The study finds that as integers grow, the relationship between consecutive square-free integers and their largest prime factors becomes clearer.
• Found results show that the number of consecutive square-free integers with increasing largest prime factors is non-zero on average.
• The mathematical approach builds upon Erdős and Pomerance’s proof, incorporating deeper insights into square-free integers.
• Implications support ongoing exploration in number theory regarding the distribution of prime factors in integer sequences.