Let \(\tau(n)=\sum_{d|n} 1\) be the divisor function. As a quadratic analogue of the Titchmarsh problem, in the paper under review, the author proves that for \(N\) large enough \[ \sum_{p^2+q^2\leq N}\tau(p^2+q^2+1)=C\,\frac{N}{\log N}\left(1+O\left(\frac{\log\log N}{\log N}\right)\right), \] where \(p,q\) are primes and the constant \(C\) is given by \[ C=\frac{\pi}{4}\prod_{p>2}\left(1-\frac{1+3p(\frac{-1}{p})}{p(p-1)^2}\right). \]