Sum Over Non-Coprime Indexes

[Leroy Quet]

I just submitted these two sequences.
(Calculated by hand, so hopefully I didn't err.)

>%S A124385 1,1,1,0,1,-1,1,1,1,-1,1,-1,1,1,1,1,1,-3,1,1,1
>%N A124385 For all n>=2, sum{2<=k<=n, GCD(k,n)>1} a(k) = 1. 
>a(1)=1.
>%e A124385 The positive integers which are <= 12 and are not coprime to 
>12 are 2,3,4,6,8,9,10,12. And a(12) is such that 
>a(2)+a(3)+a(4)+a(6)+a(8)+a(9)+a(10)+a(12) = 1.
>%Y A124385 A124386
>%O A124385 1
>%K A124385 ,more,nonn,


>%S A124386 1,2,3,2,5,-1,7,5,7,-3,11,-3,13,5,7,9,17,-15,19,7
>%N A124386 For all n>=2, sum{2<=k<=n, GCD(k,n)>1} a(k) = n. 
>a(1)=1.
>%e A124386 The positive integers which are <= 12 and are not coprime to 
>12 are 2,3,4,6,8,9,10,12. And a(12) is such that
>a(2)+a(3)+a(4)+a(6)+a(8)+a(9)+a(10)+a(12) = 12.
>%Y A124386 A124385
>%O A124386 1
>%K A124386 ,more,nonn,


First question -- I know 20 terms is not a significantly sized sample, 
but I notice that, for the terms given, a term in the first sequence is 
negative if and only if the corresponding term in the second sequence is 
also negative.
Does this pattern continue forever?
(I bet that, not only does the pattern not last, but that it breaks 
relatively soon.
But I am just guessing.)

Second question -- I include the "a(1) = 1" in the N-lines basically for 
psychological reasons. I am betting that if someone has come up with a 
sequence similar to one of the above sequences, and he/she starts their 
sequence at term 1 (instead of at the mathematically desirable offset of 
2), then he/she will likely (but not certainly) define a(1) as 1 when 
doing a look-up. And I include the a(1)=1 because:
1) it does not take from the accuracy of the rest of the sequence.
2) If someone checks the OEIS for their sequence, and they start their 
sequence at a(1), then I want it to be likely (even though it is not 
guaranteed) that they will get the sequence from the look-up.
Otherwise my sequence would not come up.
(This shows why it is a good idea to exclude the first term or two when 
looking for a match on the OEIS.)

Is doing this a good idea, or should I have started my sequences with 
a(2)?


Thanks,
Leroy Quet