Hello Don, I think you've accidentally missed all major points of contention and criticism.
I must first correct you in that I am not a mathematician. The extent of my education in math was calc2 in college 10 years ago, and I've not kept current with any publications in the area of study since.
Secondly, I believe successful communication relies on a common understanding of the terms used to communicate.
I don't mind if you use the term divisor or factor, or "proper divisor" or "proper factor" so long as you make clear what it is you are referring to. In specific cases, "proper factor" can be defined as to exclude the number 1 and "divisor" can be defined as to include negatives.
To define the restricted divisor function (i.e. aliquot sum) avoiding these two issues it can be defined as "the sum of all positive proper divisors" and a perfect number can be defined as "a positive integer which is the sum of its proper positive divisors”
The first thing I did when responding to your topic of perfect numbers was to define my terms:
Quote:
Originally Posted by modest
The divisors of 6 are {-6,-3,-2,-1,1,2,3,6}. A perfect number is “a positive integer which is the sum of its proper positive divisors”—proper meaning to exclude the number itself. The proper positive divisors of 6 are then {1,2,3}.
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I later gave two more definitions of "perfect number". It is a number which is equal to its restricted divisor function, s(n), (i.e. aliquot sum). Or, a number which is equal to half its divisor function,
. I will now give examples to clarify:
The number 12 is not perfect because,
The number 28 is perfect because,
If it is at all unclear how I am using these terms then I will break it down further. If you wish to use terms differently (or use different terms altogether) then I encourage you to define them.
~modest
