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[N. J. A. Sloane]

 From felice.russo at katamail.com  Fri Aug 31 11:35:17 2001
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From: felice.russo at katamail.com
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To: njas at research.att.com
Subject: unitary untouchable numbers
Date: Fri, 31 Aug 2001 17:35:09 +0200
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Status: R

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