Broughan, K A & Zhou, Q.(2007). Odd multiperfect numbers of abundancy 4. Journal of Number Theory, 128(6), 1566-1575.
Permanent Research Commons link: http://hdl.handle.net/10289/1796
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.
This is an author’s version of an article published in the journal: Journal of Number Theory. ©2007 Elsevier B.V.