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From: dxm@lanl.ARPA
Newsgroups: net.math
Subject: Re: Can you prove/disprove this?
Message-ID: <34214@lanl.ARPA>
Date: Tue, 3-Dec-85 11:25:36 EST
Article-I.D.: lanl.34214
Posted: Tue Dec  3 11:25:36 1985
Date-Received: Thu, 5-Dec-85 06:49:38 EST
References: <34080@lanl.ARPA> <687@spar.UUCP>
Distribution: net
Organization: Los Alamos National Laboratory
Lines: 22

> In article <34080@lanl.ARPA> dxm@lanl.ARPA writes:
> >that numbers of the form 
> >
> >		x = 2^(n-1) * (2^n - 1)
> >
> >are perfect if n is a prime number.  This was true up to the largest
> >integer the machine could represent.  
> >
  
> It is rumoured that even Euclid knew the first part of this one.  Note
> that for n=4 we have x = 120.  Let sigma(y) denote the sum of all
> positive divisors of y - e.g., sigma(6)=1+2+3+6.  Then y is perfect
> if sigma(y)=2*y.  However, sigma(120)=3*120 so 120 is referred to as
> 3-perfect, not perfect.  Did you run this on a 2 bit computer?

Actually I ran it on a Radio Shack Color Computer ( Motorola 6809 ) using
a simple 16 bit integer representation scheme.  I think the reason I
didn't catch the "n=4, therefore x=120 which isn't perfect" error is that
4 isn't prime to begin with....so of course I didn't use it.

Yours for care in reading the question, :-)
Doug Miller