Any results on $\gcd(N^2, D(N^2))$ where $N^2$ is deficient and $$D(N^2)=2N^2 - \sigma(N^2)$$ is the deficiency of $N^2$?

I checked OEIS sequence A033879 and have so far been able to get hold of Klyve, et. al's paper titled "*On the difference between an integer and the sum of its proper divisors*". Google does not appear to be of much help either.