In number theory, the Carmichael function of a positive integer n, denoted λ(n), is defined as the smallest integer m such that

for every integer a that is coprime to n.

This function can also be defined recursively, as follows.

For prime p and positive integer k such that or :

λ(p^k) = p^{k - 1}(p - 1).

For integer ,

λ(2^k) = 2^{k - 2}.

For distinct primes and positive integers :

where lcm denotes the least common multiple.

See also

• Carmichael's theorem
• Euler's phi function