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The Carmichael function is named after the American mathematician [[Robert Daniel Carmichael|Robert Carmichael]] who defined it in 1910.<ref>
{{cite journal |first1=Robert Daniel |last1=Carmichael |year=1910 |title=Note on a new number theory function |journal=Bulletin of the American Mathematical Society |volume=16 |number=5 |pages=
</ref> It is also known as '''Carmichael's λ function''', the '''reduced totient function''', and the '''least universal exponent function'''.
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===Image of the function===
The set of values of the Carmichael function has counting function<ref>{{cite journal | arxiv=1408.6506 | title=The image of Carmichael's ''λ''-function | first1=Kevin | last1=Ford | first2=Florian | last2=Luca | first3=Carl | last3=Pomerance | date=27 August 2014 | doi=10.2140/ant.2014.8.2009 | volume=8 | issue=8 | journal=Algebra & Number Theory | pages=2009–2026| s2cid=50397623 }}</ref>
:<math>\frac{x}{(\ln x)^{\eta+o(1)}} ,</math>
where
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