Chemistry - Carmichael function

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

$a^m \equiv 1 \pmod{n}$

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 $p \ge 3$ or $k \le 2$ :

λ(p k) = p k - 1 (p - 1).

For integer $k \ge 3$ ,

λ(2 k) = 2 k - 2 .

For distinct primes $p_1,p_2,\ldots,p_t$ and positive integers $k_1,k_2,\ldots,k_t$ :

$\lambda(p_1^{k_1} p_2^{k_2} \cdots p_t^{k_t}) = \mathrm{lcm}( \lambda(p_1^{k_1}), \lambda(p_2^{k_2}), \cdots, \lambda(p_t^{k_t}) )$

where $lcm$ denotes the least common multiple.

Carmichael function