When is $\lambda (n)$ = $\phi (n)$?

Question

$\lambda (n)$ is the Carmichael function and $\phi (n)$ is the Euler totient function. I can see that if $n$ is prime then the two functions agree and also if $n$ is a power of a prime they agree. Are there any other cases when they agree?

Answer 1

$\lambda (n)$ is the exponent of $U(n)=(\mathbb Z/ n \mathbb Z)^\times$, the group of units mod $n$.

By the fundamental theorem of finite abelian groups, $U(n)$ has an element of order $\lambda (n)$. Therefore, $\lambda (n)=\phi (n)$ iff $U(n)$ is cyclic, which happens iff $n=1, 2, 4, p^k,2p^k$, where $p$ is an odd prime.