Sum of primitive roots

[Robert Israel]

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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