Abstract
A survey is given of the attitude to and use of the concepts of deficient, perfect, and abundant number from the time of Nicomachus of Gerasa to that of David Anakht and Alcuin of York. Alcuin's ‘Letter to Dafnin', the source of an anecdote frequently mentioned in mathematical texts, is included as an appendix.The statistics of deficient, perfect, and abundant numbers over the range 1–50000 are studied and presented graphically in several novel ways and compared with the work of Davenport and others on the distribution-law for the values of z = σ (n)/(2n).Some queries are raised concerning observations which ancient writers might have been expected to make; for example, did they notice that about one half of all the even numbers are abundant?
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.