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Carmichael function

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In the Carmichael function is the smallest number so that for every that is coprime to . The namesake is Robert Daniel Carmichael (1879—1967).

Calculation of the Carmichael function

means distinct primes and means natural numbers.
The function is available in Mathematica as "CarmichaelLambda[n]".

Carmichael function and Euler totient function

The Carmichael function is a divisor of Euler's totient function . For 1 and every prime number the Carmichael function is equal to the Euler's totient function

Example of difference

  • Euler's totient function:
  • Carmichael function:


The Carmichael function (Cf. A002322):

{1, 1, 2, 2, 4, 2, 6, 2, 6, 4, 10, 2, 12, 6, 4, ...}

See also