Re: why there are no Odd Perfect Numbers (not including 1) Re:

In article <1127265902.817448.63360@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mensanator@xxxxxxxxxxx <mensanator@xxxxxxx> wrote:
>
>Gerry Myerson wrote:
>> In article <In2HEF.D8u@xxxxxx>, "*** T. Winter" <***.Winter@xxxxxx>
>> wrote:
>>
>> > Wrong. Take 945. The sum of its proper divisors is 975, or about 103 %
>> > of the original number. Or take 33426748355, the sum of the proper
>> > divisors is 33459293244 (if I did do my calculations correctly)
>>
>> 33426748355 is not a square (no square ends in 55), so it has an even
>> number of divisors, so an odd number of proper divisors, and they're
>> all odd, so their sum is odd, so it can't be 33459293244.

>Dammit, I gotta know!

.... [Lots of work] ...

In Maple, you just say

> numtheory[sigma](33426748355)-33426748355;

and the result, in the blink of an eye, is 33459293245.

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada



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