PlanetMath: quasiperfect number

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quasiperfect number

(Definition)

If there exists an abundant number with divisors $d_1, \ldots, d_k$ , such that

$\displaystyle \sum_{i = 1}^k d_i = 2n + 1,$

that number would be called a quasiperfect number. Such a number would be $n > 10^{35}$ and have $\omega(n) > 6$ (where $\omega$ is the number of distinct prime factors function).

A quasiperfect number would thus overshoot the mark for being a perfect number by a margin of just 1. (The powers of 2 are short of perfection by a margin of 1).

"quasiperfect number" is owned by CompositeFan.

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See Also: almost perfect number

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Cross-references: margin, perfect number, number of distinct prime factors function, number, divisors, abundant number
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This is version 3 of quasiperfect number, born on 2006-07-20, modified 2006-10-02.
Object id is 8160, canonical name is QuasiperfectNumber.
Accessed 852 times total.

Classification:

AMS MSC:

11A05 (Number theory :: Elementary number theory :: Multiplicative structure; Euclidean algorithm; greatest common divisors)

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