Science > Physics > ancient aliquot category: abundant, deficient, perfect (number theory) - two questions
| Topic: |
Science > Physics |
| User: |
"mountain man" |
| Date: |
03 May 2004 04:41:10 AM |
| Object: |
ancient aliquot category: abundant, deficient, perfect (number theory) - two questions |
Also posted to sci.mathematics.
I have a question related to the (extended) history of mathematics
relating to the definition and use of the terms abundant, deficient
and perfect.
AFAIK abundant numbers and perfect numbers and other series
related to these are defined according to the summation of their
constituent factors. eg: 1+2+3 = 6 is a perfect number (1,2,3)
being the factors of 6.
QUESTION 1: Is anyone out there aware of any precedent
in which such definition (specifically "abundance") considers
something other than "summation" of the components?
Specifically, I have done some computational research using an
alternate definition of "abundance, deficient, perfect" in ordered
factorisations. (Ordered factorisations cannot be summed).
The definition employed is by way of *number of ordered
factorisations", and the (rather surprising - to me) results
and conclusions have been published here:
http://www.mountainman.com.au/harmonics_01.htm
QUESTION 2: Can anyone advise me the name of the
corresponding term in the Indian mathematical system
to that of "aliquot part" in the Greek?
Thanks for any insight provided.
Pete Brown
Falls Creek
Oz
www.mountainman.com.au
.
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