[padjxvzc] Factoring midpoints of twin primes

OEIS A014574.  These numbers strike me as smoother than typical numbers, but that may be an illusion.

4 Mat([2, 2])
6 [2, 1; 3, 1]
12 [2, 2; 3, 1]
18 [2, 1; 3, 2]
30 [2, 1; 3, 1; 5, 1]
42 [2, 1; 3, 1; 7, 1]
60 [2, 2; 3, 1; 5, 1]
72 [2, 3; 3, 2]
102 [2, 1; 3, 1; 17, 1]
108 [2, 2; 3, 3]
138 [2, 1; 3, 1; 23, 1]
150 [2, 1; 3, 1; 5, 2]
180 [2, 2; 3, 2; 5, 1]
192 [2, 6; 3, 1]
198 [2, 1; 3, 2; 11, 1]
228 [2, 2; 3, 1; 19, 1]
240 [2, 4; 3, 1; 5, 1]
270 [2, 1; 3, 3; 5, 1]
282 [2, 1; 3, 1; 47, 1]
312 [2, 3; 3, 1; 13, 1]
348 [2, 2; 3, 1; 29, 1]
420 [2, 2; 3, 1; 5, 1; 7, 1]
432 [2, 4; 3, 3]
462 [2, 1; 3, 1; 7, 1; 11, 1]
522 [2, 1; 3, 2; 29, 1]
570 [2, 1; 3, 1; 5, 1; 19, 1]
600 [2, 3; 3, 1; 5, 2]
618 [2, 1; 3, 1; 103, 1]
642 [2, 1; 3, 1; 107, 1]
660 [2, 2; 3, 1; 5, 1; 11, 1]
810 [2, 1; 3, 4; 5, 1]
822 [2, 1; 3, 1; 137, 1]
828 [2, 2; 3, 2; 23, 1]
858 [2, 1; 3, 1; 11, 1; 13, 1]
882 [2, 1; 3, 2; 7, 2]
1020 [2, 2; 3, 1; 5, 1; 17, 1]
1032 [2, 3; 3, 1; 43, 1]
1050 [2, 1; 3, 1; 5, 2; 7, 1]
1062 [2, 1; 3, 2; 59, 1]
1092 [2, 2; 3, 1; 7, 1; 13, 1]
1152 [2, 7; 3, 2]
1230 [2, 1; 3, 1; 5, 1; 41, 1]
1278 [2, 1; 3, 2; 71, 1]
1290 [2, 1; 3, 1; 5, 1; 43, 1]