Odd multiperfect numbers of abundancy 4

Broughan, Kevin A.; Zhou, Qizhi

doi:10.1016/j.jnt.2007.02.001

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Broughan, K A & Zhou, Q.(2007). Odd multiperfect numbers of abundancy 4. Journal of Number Theory, 128(6), 1566-1575.

Permanent Research Commons link: https://hdl.handle.net/10289/1796

Abstract

Euler's structure theorem for any odd perfect number is extended to odd multiperfect numbers of abundancy power of 2. In addition, conditions are found for classes of odd numbers not to be 4-perfect: some types of cube, some numbers divisible by 9 as the maximum power of 3, and numbers where 2 is the maximum even prime power.

Date

2007

Type

Journal Article

Publisher

Elsevier

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Computing and Mathematical Sciences Papers [1455]