An important unsolved question in number theory is the Lehmer's totient problem that asks whether there exists any composite number n such that φ(n)∣n−1, where φ is the Euler's totient function. It is known that if any such n exists, it must be odd, square-free, greater that 1030
Nearby in the stack
, and divisible by at least
15
distinct primes. Such a number must be also a Carmichael number. In this short note, we discuss a group-theoretical analogous problem involving the function that counts the number of automorphisms of a finite group. Another way to generalize the Lehmer's totient problem is also proposed.
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