In[1]:= AbsoluteTiming[
 p = 25*10^6;

 f[a_] := Module[{myList, lm, chk},
   myList = Divisors[(a + 1) (a - 1)];
   lm = Length@myList;
   chk[k_] := Module[{x = myList[[k]], y = myList[[lm + 1 - k]]},
     Return[EvenQ[y - x] && a > x && a + y <= p && a <= (y - x)/2]];
   Return[Length@Select[Range[lm/2], chk]]];

 ans = Parallelize@Sum[f[a], {a, 2, Floor[p/(2 + Sqrt[2])]}] +
   Floor[(p - 1)/2]]

Out[1]= {1358.6, 61614848}