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The abundance of a number $n$ is the quantity


where $\sigma(n)$ 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 $n$ based on the value of $A(n)$.

$A(n)$ Number
$<0$ Deficient Number
$-1$ Almost Perfect Number
0 Perfect Number
1 Quasiperfect Number
$>0$ Abundant Number

See also Deficiency


Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 45-46, 1994.

© 1996-9 Eric W. Weisstein