Abundance
The abundance of a number 
is the quantity
where
is the Divisor Function. Kravitz has conjectured that no numbers exist whose abundance isan Odd Square (Guy 1994).The following table lists special classifications given to a number based on the value of 
.
| Number |
 | Deficient Number |
 | Almost Perfect Number |
| 0 | Perfect Number |
| 1 | Quasiperfect Number |
 | Abundant Number |
References
Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 45-46, 1994.