Unitary perfect numbers are Zumkeller

A positive integer is said to be unitary perfect if it is the sum of its proper unitary divisors. A number is Zumkeller if its set of divisors can be partitioned into two sets having the same sum. In the OEIS entry relative to unitary perfect numbers, the following conjecture is posed: are all unitary perfect numbers Zumkeller? This statement has been verified for the known unitary perfect numbers. In this paper, we prove that this conjecture is true by showing that every unitary perfect number is practical and has an even sum of divisors.