On local laws for the number of small prime factors

TL;DR

This paper studies how small prime factors are distributed among integers, focusing on the transition phase for certain parameter values, and addresses a question posed by Alladi.

Contribution

It provides a detailed description of the local distribution of small prime factors, highlighting the transition phase for specific parameter ranges.

Findings

Characterizes the local distribution of small prime factors.

Identifies the transition phase in the distribution.

Addresses Alladi's question on prime factor distribution.

Abstract

Investigating a question of Alladi, we describe the local distribution of small prime factors of integers, with emphasis on the transition phase occurring for certain values of the parameters.