Vol. 8, No. 8, 2014

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The image of Carmichael's $\lambda$-function

Kevin Ford, Florian Luca and Carl Pomerance

Vol. 8 (2014), No. 8, 2009–2026
Abstract

We show that the counting function of the set of values of Carmichael’s λ-function is x(logx)η+o(1), where η = 1 (1 + loglog2)(log2) = 0.08607.

Keywords
Carmichael's function, Carmichael's lambda function
Mathematical Subject Classification 2010
Primary: 11N64
Secondary: 11A25, 11N25
Milestones
Received: 23 June 2014
Revised: 4 September 2014
Accepted: 9 October 2014
Published: 28 November 2014
Authors
Kevin Ford
Department of Mathematics
University of Illinois at Urbana–Champaign
1409 West Green Street
Urbana, IL 61801
United States
Florian Luca
School of Mathematics
University of the Witwatersrand
P.O. Box Wits 2050
Johannesburg
South Africa Instituto de Matématicas
UNAM Juriquilla
Santiago de Querétaro, 76230
Querétaro de Arteaga
México
Carl Pomerance
Mathematics Department
Dartmouth College
Kemeny Hall
Hanover, NH 03755
United States