A unitary perfect number is an integer which is the sum of its positive proper unitary divisors, not including the number itself.

Thus, 60 is a unitary perfect number, because its unitary divisors, 1, 3, 4, 5, 12, 15 and 20 are its proper unitary divisors, and 1 + 3 + 4 + 5 + 12 + 15 + 20 = 60. The first few unitary perfect numbers are

6, 60, 90, 87360, 146361946186458562560000

There are no odd unitary perfect numbers, the sums of their unitary divisors always fall short. It's not known whether or not there are infinitely many even unitary perfect numbers.

See also: perfect number