Does OEIS sequence A252502 contain all even numbers which are totients and all odd numbers n$n$ with n−1$n-1$ totients?

For even number n$n$, if n$n$ is not a totient (i.e. not in the range of Euler totient function), then n$n$ is not in OEIS sequence A252502, but if n$n$ is a totient, must be n$n$ in A252502?

For odd number n$n$, if n−1$n-1$ is not a totient (i.e. not in the range of Euler totient function), then n$n$ is not in OEIS sequence A252502 (except n=1$n=1$), but if n−1$n-1$ is a totient, must be n$n$ in A252502?

If this conjecture is true, then the famous conjecture that there is no n$n$ such that there is only one x$x$ whose Euler totient function is n$n$ is also true.