OEIS A064740
Mathematica code written by Michael De Vlieger, St. Louis, Missouri, 2021 1207.
Based on LRS Algorithm described on page 4-5 of Lagarias-Rains-Sloane 2002 (http://arXiv.org/abs/math.NT/0204011)

Block[{nn = 2^16, c, h, j, k, m, n, p, a020639, a032742, a073735}, 
 c[_] = h[_] = a020639[_] = a032742[_] = 0; m = j = c[2] = 2; 
 Array[Set[h[#], 1] &, 2];
 Monitor[Do[
   Set[{a020639[i], a032742[i]}, {#1[[1, 1]], 
       Times @@ Power @@@ #2}] & @@ TakeDrop[FactorInteger[i], 1], {i,
     nn}], i]; 
 a073735 = {1}~Join~Most@ Reap[
     Monitor[Do[
       If[m == nn, Break[], k = nn; 
        While[m > 1, Set[p, a020639[m]]; Set[k, Min[k, c[p]]]; 
         Set[m, a032742[m]]]; Sow[GCD[j, k]]; Set[h[k], 1]; 
        Map[If[c[#] == 0, 
           Set[c[#], #], (Set[n, c[#]/#]; While[h[# n] > 0, n++]; 
            Set[c[#], # n])] &, FactorInteger[k][[All, 1]]]; 
        m = j = k], {i, 3, nn}], i]][[-1, -1]];
 Map[FactorInteger[#][[1, 1]] &, a073735[[2 ;; 10^4]] ] ]