Sum Over Coprime Integers = 0 (or 1)

[Leroy Quet]

I am reposting the email below.
I apologize if this message appears twice.

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Let the sequence {a(k)} be such that

a(1) = 1;

For each m >= 3,

0 = sum{1<=k<m,GCD(k,m)=1} a(k).

I get, by hand, the sequence beginning:

1, -1, -1, 1, -1, 1, 1, -1, -1,...


Is there a closed form for this sequence?

It is doubtful, especially since I only have 10 terms above, but could it 
be that every term is either 1 or -1?
(I bet a counterexample, if one exists, is EASILY found.)
:)

thanks,
Leroy Quet