Carmichael function: Difference between revisions

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for every integer {{mvar | a}} between 1 and {{mvar | n}} that is [[coprime]] to {{mvar | n}}. In algebraic terms, {{math | ''λ''(''n'')}} is the [[exponent of a group|exponent]] of the [[multiplicative group of integers modulo n|multiplicative group of integers modulo {{mvar | n}}]].

The Carmichael function is named after the American mathematician [[Robert Daniel Carmichael|Robert Carmichael]] andwho isdefined alsoit knownin as '''Carmichael's λ function''', the '''reduced totient function''', and the '''least universal exponent function'''.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=232-238 |doi=10.1090/S0002-9904-1910-01892-9|doi-access=free }}

</ref>. It is also known as '''Carmichael's λ function''', the '''reduced totient function''', and the '''least universal exponent function'''.

The following table compares the first 36 values of {{math | ''λ''(''n'')}} {{OEIS|id=A002322}} with [[Euler's totient function]] {{mvar | φ}} (in '''bold''' if they are different; the {{mvar | n}}s such that they are different are listed in {{oeis|A033949}}).