Quadratic residues

[Thomas Baruchel]

I asked recently about
>  a(n) is the number of divisors of (n+1)
> Have you ever seen closely-related sequences like that one?

After some hints and a
> Happy hunting!
I finally noticed this :
   a) prime numbers 4n+3 lead to the set of their quadratic residues
   b) prime numbers 4n+1 lead to the set of their quadratic non-residues
   c) odd composite numbers :
      15 --> quadratic residues
      21 --> difficult to understand at first sight
Since my datas are empirical and need much work it is difficult to get
much information. Even numbers are difficult to study also.
Have you ever heard about such a behaviour? In that case, what would
you predict for 21?

WARNING. When I speak of "quadratic residues", I mean the residue has
a GCD = 1 with the number (convention may vary).

Thank you for everything,

-- 
Thomas Baruchel