Did you check the first 1000 terms $a_n$?

Did you try asking Stephen Wolfram stephenwolfram.com?

@LSpice: The reference does not have a clear definition. If it is a standard definition, I prefer a standard reference. If it is not standard, I would like to see an explanation with examples. That should include a justification of the word "smooth".

If you think that this reference makes the situation clearer, you are wrong.

What is a smooth measure on a f.g.group?

Does $\mu$ have a finite support?

Isn't there a standard inequality between the two maxes

$a(6)=2250?{}{}{}$

If the subgroup is irreducible, that should be true and should follow from the proof of the Tits alternative.

@Aeryk: Did you look at these references?

For example $x^2+11y^2$ has discriminant $44$. So if $n$ is odd prime and not $11$ then $n$ is represented by that form iff $\left(\frac{n}{11}\right)=1$.

A prime number $n$ is represented by a binary form with discriminant $d$ iff $4d$ is a quadratic residue modulo $4n$ ($\gcd(n,d)=1$).

Did you try substituting $\Gamma(n)$ by $(n-1)!$ and using induction?