# Dorian Goldfeld

Affiliation: Columbia University

Email: goldfeld@columbia.edu

Title Of Talk: On an additive prime counting function of Alladi and Erdös

Abstract: Let $n = \prod\limits_{i=1}^r p_i^{a_i}$ be the unique prime decomposition of a positive integer $n$. In 1977, Alladi and Erdös introduced the additive function $$A(n) := \sum_{i=1}^r a_i p_i.$$ Among several other things they proved that $A(n)$ is uniformly distributed modulo 2. In this talk we will show that $A(n)$ is uniformly distributed module $q$ for any integer $q \ge 2.$