Definition:Abundancy
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Definition
Let $n$ be a positive integer.
Let $\sigma \left({n}\right)$ be the sigma function of $n$.
That is, let $\sigma \left({n}\right)$ be the sum of all positive divisors of $n$.
Then the abundancy of $n$ is defined as $\dfrac {\sigma \left({n}\right)} n$.
Abundant
A number is classified as abundant iff $\dfrac {\sigma \left({n}\right)} n > 2$.
Perfect
A number is classified as perfect iff $\dfrac {\sigma \left({n}\right)} n = 2$.
Deficient
A number is classified as deficient iff $\dfrac {\sigma \left({n}\right)} n < 2$.
Also See
Compare Abundance.
