On weird and pseudoperfect numbers

Author:

Benkoski S. J.,Erdős P.

Abstract

If n is a positive integer and σ ( n ) \sigma (n) denotes the sum of the divisors of n, then n is perfect if σ ( n ) = 2 n \sigma (n) = 2n , abundant if σ ( n ) 2 n \sigma (n) \geqq 2n and deficient if σ ( n ) > 2 n \sigma (n) > 2n . n is called pseudoperfect if n is the sum of distinct proper divisors of n. If n is abundant but not pseudoperfect, then n is called weird. The smallest weird number is 70. We prove that the density of weird numbers is positive and discuss several related problems and results. A list of all weird numbers not exceeding 10 6 {10^6} is given.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Reference7 articles.

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