On an additive arithmetic function

Krishnaswami Alladi and Paul Erdős

Vol. 71 (1977), No. 2, 275–294

DOI: 10.2140/pjm.1977.71.275

Abstract

We discuss in this paper arithmetic properties of the function A(n) = ∑ _p^α∥nαp. Asymptotic estimates of A(n) reveal the connection between A(n) and large prime factors of n. The distribution modulo 2 of A(n) turns out to be an interesting study and congruences involving A(n) are considered. Moreover the very intimate connection between A(n) and the partition of integers into primes provides a natural motivation for its study.

Mathematical Subject Classification

Primary: 10A20, 10A20

Secondary: 10A45

Milestones

Received: 29 October 1975

Revised: 29 October 1976

Published: 1 August 1977