your mail

[frusso]

It is 926.
In fact my search was done up to 10^5. 
So how I can be sure that one number is unitary untouchable?
The numbers 2 3 4 5  7 for example looks like to to be untouchable but are
we sure that above 10^5 they never will be a solution of us(x)=n?
I tryed to monitor the difference between those numbers (2,3,5,7...) and
us(x) for very large x and even though this difference in average grows
linearly with x every so often some point goes out and became very close to
zero...
Is there any theoretical approach to determine the unitary untouchable
numbers?

Rgds and thanks.  Felice
     
-----Original Message-----
From: Richard Guy [mailto:rkg at cpsc.ucalgary.ca]
Sent: Friday, August 31, 2001 7:35 PM
To: N. J. A. Sloane
Cc: seqfan at ext.jussieu.fr
Subject: Re: your mail


What is the sum of the (proper) unitary divisors of
102016 ?     R.

On Fri, 31 Aug 2001, N. J. A. Sloane wrote:

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> Subject: unitary untouchable numbers
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> Neil
> I would like to extend the concept of untouchable numbers to the unitary
divisors. So the definiton of unitary untouchable numbers should be:
> 
> The numbers n such that us(x)=n has no solution where us(x) is the sum of
unitary proper divisors of x.
> 
> With a ubasic code for n<=10^5 I have found the following ones:
> 
> 2 3 4 5 7 374 702 758 926 930 998
> 
> But how I can sure that none of those became solution of us(x)=n for
larger values of n (>10^5)?
> 
> Is there any theoretical approach to prove that a number is unitary
untouchable?
> 
> Thanks.  Felice
> 
> 

>