Sum of primitive roots

[Robert Israel]

It's interesting to note, btw, that although this sequence contains
6=2*3, 18=2*3^2, 54=2*3^3 and 162=2*3^4, it does not contain
486=2*3^5, as 47 + 65 + 77 + 83 + 101 + 113 = 486.

On Tue, 8 Jan 2008, Robert Israel wrote:

> Why not allow all the positive integers that have primitive roots, so 
> include 4, p^n and 2 p^n as candidates (for positive integers n and odd
> primes p)?
> Then I believe you get 2,3,4,6,7,9,11,14,18,22,38,54,162,...
>
> Robert Israel                                israel at math.ubc.ca
> Department of Mathematics        http://www.math.ubc.ca/~israel 
> University of British Columbia            Vancouver, BC, Canada
>
> On Tue, 8 Jan 2008, franktaw at netscape.net wrote:
>
>> 2,3,7,11.
>> 
>> These primes cannot be represented as a sum of their (distinct) 
>> primitive roots (requiring the root to be positive).  Are there any 
>> others?
>> 
>> I have checked up to p = 167.  Note that it is not necessary to check 
>> primes = 1 (mod 4), since for such primes, if k is a primitive root, so 
>> is p - k.  It seems very unlikely that there are any others, but I 
>> don't see  how to prove it.
>> 
>> Assuming that this list is complete, should this be in the OEIS?
>> 
>> Franklin T. Adams-Watters
>> 
>> 
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>