Vol. 71, No. 2, 1977

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On an additive arithmetic function

Krishnaswami Alladi and Paul Erdős

Vol. 71 (1977), No. 2, 275–294
Abstract

We discuss in this paper arithmetic properties of the function A(n) = pαnαp. 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
Authors
Krishnaswami Alladi
Paul Erdős