Aspiring Number

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.

REFERENCES:

Sloane, N. J. A. Sequence A063769 in "The On-Line Encyclopedia of Integer Sequences."