Let
where is the divisor function and is the restricted divisor function, and define the aliquot sequence of by
If the sequence reaches a constant, the constant is known as a perfect number. A number that is not perfect but whose sequence becomes constant is known as an aspiring number. For example, beginning with 25 gives the sequence 25, 6, 6, 6, ..., so 25 is an aspiring number and 6 is a perfect number.
The first few aspiring numbers are 25, 95, 119, 143, ... (OEIS A063769). It is not known if 276 is an aspiring number, though it is very unlikely for this to be the case.