Guy \cite{Gu04} reports that Carlitz, Erd\H{o}s, and Subbarao offer \$10 for settling this question, and that Subbarao offers 10 cents for each new example.

There are no odd unitary perfect numbers. There are five known unitary perfect numbers (A002827 in the OEIS):\[6, 60, 90, 87360, 146361946186458562560000.\]This is problem B3 in Guy's collection \cite{Gu04}.


References


[Gu04] Guy, Richard K., Unsolved problems in number theory. (2004), xviii+437.