The conjecture on the classification of unitary perfect numbers

A positive integer $n$ is unitary perfect when its unitary divisor sum satisfies $\sigma^*(n)=2n$, where the unitary divisors are the divisors $d$ such that $\gcd(d,n/d)=1$. The known unitary perfect numbers are

$$6, 60, 90, 87360, 146361946186458562560000.$$

The classification conjecture. The five integers above are the only unitary perfect numbers. No further unitary perfect number is known; this is the classical Subbarao–Warren problem, and the paper provides bounded-box reductions and computational evidence but does not prove the classification.