At the end of a Monthly note, Beiter conjectured the following.
Let $p<q<r$ be primes greater than $3$. Writing the $pqr$-th cyclotomic polynomial as $$\Phi_{pqr} (x)= \sum c_nx^n$$ With $c_{\phi(pqr)}=1$, we have $|c_n| \leq \frac 12 (p+1)$ for all primes $q,r$.
Actually, he conjectures $\frac 12(p+1)$ is an upper bound for $c_n$, but I believe he meant $|c_n|$.
This note was published in 1968. Has this conjecture been settled/has there been analysis on the coefficients of $\Phi_n$ for squarefree $n$ with exactly three factors?