least universal exponent

There are two definitions of the Carmichael function. One is the reduced totient function (also called the least universal exponent function), defined as the smallest integer λ(n) such that k^(λ(n)) congruent 1 (mod n) for all k relatively prime to n. The multiplicative order of a (mod n) is at most λ(n). The first few values of this function, implemented as CarmichaelLambda[n], are 1, 1, 2, 2, 4, 2, 6, 2, 6, 4, 10, ... (OEIS A002322). It is given by the formula λ(n) = LCM[(p_i - 1) p_i^(α_i - 1)]_i, where p_i^(α_i) are primaries.

modulo multiplication group | totient function