Carmichael function
There are two different functions that are both called Carmichael function. It is similar to the totient function
The first definition
The first definition is also called the reduced totient function or the least universal exponent function. It is defined as the smallest positive integer such that for all positive integers relatively prime to . The modulo order of is less than or equal to .
Suppose . We have
Examples
The second definition
The second definition of the Carmichael function is the least common multiples of all the factors of . It is written as . However, in the case , we take as a factor instead of .