The abundance of a number is the quantity

where is the Divisor Function. Kravitz has conjectured that no numbers exist whose abundance is an 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.

© 1996-9

1999-05-25