I'm trying to find all values of $n$ that satisfy euler's phi function in the title.
I start by knowing $n$ cannot be a power of $2$ since $\phi (n)$ is not. Then, $n$ is divisible by an odd prime.
I try to find odd primes satisfying $(p-1)|20$ and so my list is $3,5,11$. Then, $n=2^a3^b5^c11^d$. I'm stuck here, since I don't know how to bound my exponents or what values to use.
I think $a\leq 2$ because $2^2|\phi(n)$. So far I have generated:
$n=2^2\cdot 11, 2\cdot 3\cdot 11, 3\cdot 11$, or $44,66,33$. This was done through trial and error i.e. sampling values for exponents and checking if they satisfy the phi function. Is there an algebraic way to determine the exponents / check if there are other solutions?