On an additive prime divisor function of Alladi and Erdos

TL;DR

This paper investigates the additive prime divisor function introduced by Alladi and Erdős, demonstrating its uniform distribution modulo any fixed integer, thereby advancing understanding of its probabilistic properties.

Contribution

The paper proves that the additive prime divisor function is uniformly distributed modulo any fixed integer, providing new insights into its distributional behavior.

Findings

A(n) is uniformly distributed mod q for any fixed q > 1

The distributional properties of A(n) are characterized

Advances understanding of additive prime divisor functions

Abstract

This paper discusses the additive prime divisor function $A(n) := \sum\limits_{p^\alpha || n} \alpha \, p$ which was introduced by Alladi and Erd\H os in 1977. It is shown that $A(n)$ is uniformly distributed (mod $q$) for any fixed integer $q > 1.$