An integer n is called a super unitary perfect number if σ^*(σ^*(n)) = 2n, where σ^*(n) is the unitary divisor function. The first few are 2, 9, 165, 238, 1640, ... (OEIS A038843). It is not known if there exist any odd super unitary perfect numbers other than 9 and 165.

unitary divisor function | unitary perfect number