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Odd multiperfect numbers of abundancy 4

Authors
Journal
Journal of Number Theory
0022-314X
Publisher
Elsevier
Publication Date
Volume
128
Issue
6
Identifiers
DOI: 10.1016/j.jnt.2007.02.001
Keywords
  • Odd Multiply Perfect Number
  • Abundancy
  • Euler Factor
Disciplines
  • Mathematics

Abstract

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.

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