Browsing by Author "Zhou, Qizhi"

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Divisibility by 3 of even multiperfectnumbers of abundancy 3 and 4

Broughan, Kevin A.; Zhou, Qizhi (2010)

We say a number is flat if it can be written as a non-trivial power of 2 times an odd squarefree number. The power is the “exponent” and the number of odd primes the “length”. Let N be flat and 4-perfect with exponent a ...
Flat primes and thin primes

Broughan, Kevin A.; Zhou, Qizhi (2010)

A number is called upper (lower) flat if its shift by +1 ( −1) is a power of 2 times a squarefree number. If the squarefree number is 1 or a single odd prime then the original number is called upper (lower) thin. Upper ...
Multiply perfect numbers of low abundancy

Zhou, Qizhi (University of Waikato, 2010)

The purpose of this thesis is to investigate the properties of multiperfect numbers with low abundancy, and to include the structure, bounds, and density of certain multiperfect numbers. As a significant result of this ...
Odd multiperfect numbers of abundancy 4

Broughan, Kevin A.; Zhou, Qizhi (Elsevier, 2007)

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, ...