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A number 
which is the sum of its Unitary Divisors with the exception of itself.
There are no Odd unitary perfect numbers, and it has been conjectured that there are only a Finite number of
Even ones. The first few are 6, 60, 90, 87360, 146361946186458562560000, ... (Sloane's A002827).
References
Guy, R. K. ``Unitary Perfect Numbers.''
§B3 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 53-59, 1994.
Sloane, N. J. A. Sequence
A002827/M4268
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.
Wall, C. R. ``On the Largest Odd Component of a Unitary Perfect Number.'' Fib. Quart. 25, 312-316, 1987.