[seqfan] A006521 and n dividing 2^n+1, but not 2^(n-1)+1

[Rainer Rosenthal]

In http://www.research.att.com/~njas/sequences/A006521 they say:

                   For a proof, see [1]

I think this simply means the first of the references given, but
it would be a good idea to have the numbers [1], [2] etc. in
front of the references, just in case someone happened to add another
reference.

I admit that this is nitpicking squared and so I go straight on to
what I'm really interested in: 

          according to A006521 there are many                (1)
          numbers n which divide 2^n+1.

In a discussion in de.rec.denksport I learned that 


          no n > 1 does exist such that                      (2)
          n divides 2^(n-1)+1.

I couldn't find any sequence related to this fact. I would like to
see a proof for (2).

Cheers,
Rainer