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Using an extension of the abundancy index to imaginary quadratic rings with unique factorization, we define what we call n-powerfully perfect numbers in these rings. This definition serves to extend the concept of perfect numbers that have been defined and studied in the integers. We investigate the properties of 2-powerfully perfect numbers in the rings and the three imaginary quadratic rings with unique factorization in which 2 is not a prime.
- Abundancy index
- Quadratic ring
- Solitary number
- Perfect number
- Primary 11R11
- Secondary 11N80
- Defant, C. (2014) An extension of the abundancy index to certain quadratic rings, Int. J. Math Comput. Sci. 9, 63–82.
- Defant, C. (2014) Multiperfect numbers in certain quadratic rings, Int. J. Math Comput. Sci. 9, 49–61
- Stark, H. M. (1967) A complete determination of the complex quadratic fields of classnumber one. Michigan Math. J. 14 1–27.
Cite this paper
Defant, C. (2017). On 2-powerfully perfect numbers in three quadratic rings. Notes on Number Theory and Discrete Mathematics, 23(2), 1-11.