A google search will find you the OEIS sequence: https://oeis.org/A147811, which gives a nice formula for generating Alexandrian Integers, "The numbers are of the form p(p+d)(p+(p^2+1)/d), where d runs over divisors of p^2+1 and p runs over all positive integers.", below is a proof for this formula.
Now we can run p over the integers, calculate the divisors of p*p + 1 and find all the corresponding Alexandrian integers (We also note that we only need to calculate the Alexandrian integers for the first half of the divisors because if p*p - 1 = ab then A1 = p(p+a)(p+(p^2+1)/a) = p(p+a)(p+b) = p(p+b)(p+(p^2+1)/b) = A2)
However we must crucially note that they will not be generated in order!!
I trial and errored and found that generating 500,000 alexandrian integers using the above method gets the correct answer.
No interactive code for this problem, my code is given below