Consider the symmetric boolean function $$F(x_1,\dots,x_n)=1\iff\sum_{i=1}^nx_i\mbox{ is a square}.$$
It is implementable in $TC^0$.
Is there an $ACC^0$ implementation?
The reason I ask is there seems to be few tricks which can be deployed.
Square is sum of consecutive odd numbers.
Square is $0$ or $1$ mod $4$ (checkable by $\oplus$ gates).
Squares are the set of the integers having odd number of divisors.
Few are available in https://proofwiki.org/wiki/Category:Square_Numbers.
But is there a finite number of tricks which capture the function and place it in $ACC^0$?