On the normal number of prime factors of \(\phi(n)\)
type: Item
instance of: scholarly article
title: On the normal number of prime factors of \(\phi(n)\)
zbMATH Open document ID: 0617.10037
DOI: 10.1216/RMJ-1985-15-2-343
author: Carl Pomerance
author: P. Erdős
published in: Rocky Mountain Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: The authors prove that the number of prime factors (either distinct or counted with multiplicities) of Euler's function \(\phi(n)\) obeys the Gaussian distribution law. The normal order equals \((\log\log n)^3/2\) and the standard deviation is \(3^{-1/2}(\log\log n)^{3/2}\).
Mathematics Subject Classification ID: 11K65
Mathematics Subject Classification ID: 11N37
zbMATH DE Number: 4000050
zbMATH Keywords: Euler phi-function
zbMATH Keywords: number of prime factors
zbMATH Keywords: normal order
zbMATH Keywords: standard deviation
Wikidata QID: Q105890387
reviewed by: Władysław Narkiewicz
MaRDI profile type: Publication
full work available at URL: rmj-1985-15-2-343
OpenAlex ID: W2018226616
description: scientific article; zbMATH DE number 4000050