Puzzle 734. "Common Sigma, Uncommon Clique" Numbers

My friend Fred Schneider propose the following puzzle:

I have come across an interesting sequence while trying to solve a different problem.
I was wondering if any readers would like to try to extend it.

A239635 (I just submitted it so I think it's still being reviewed)

"Common Sigma, Uncommon Clique" Numbers

The n-th term is the minimum number s where exists a set of n numbers which each have sigma = s (Common Sigma) and which are all relatively prime to each other (Uncommon Clique).

Here are the first 32 terms:
1, 12, 24, 72, 240, 360, 1440, 1440, 1440, 8640, 10080, 15120, 34560, 45360, 55440, 60480, 60480, 166320, 181440, 211680, 332640, 332640, 332640, 665280, 665280, 665280, 831600, 907200, 1663200, 2494800, 2661120, 2661120

And, for the first 5 terms, here are the solutions sets (and member factors which show the sets are mutually relatively prime):

1) 1 :
1 = 1

2) 12 :
6 = 2 * 3
11 = 11

3) 24 :
14 = 2 * 7
15 = 3 * 5
23 = 23

4) 72 :
46 = 2 * 23
51 = 3 * 17
55 = 5 * 11
71 = 71

5) 240 :
135 = 3^3 * 5
158 = 2 * 79
203 = 7 * 29
209 = 11 * 19
239 = 239

and similar details on the last (32nd) term I have found:

32) 2661120 :
1126240 = 2^5 * 5 * 7039
1667601 = 3^3 * 13 * 4751
2306549 = 7 * 109 * 3023
2420407 = 11 * 139 * 1583
2498269 = 17 * 223 * 659
2514023 = 19 * 307 * 431
2534629 = 29 * 71 * 1231
2550217 = 23 * 110879
2550773 = 31 * 107 * 769
2566111 = 43 * 83 * 719
2572709 = 41 * 131 * 479
2599021 = 79 * 167 * 197
2605633 = 47 * 55439
2611787 = 53 * 49279
2616709 = 59 * 44351
2631463 = 89 * 29567
2640203 = 127 * 20789
2646157 = 179 * 14783
2647069 = 191 * 13859
2649793 = 239 * 11087
2650309 = 251 * 10559
2650777 = 263 * 10079
2654633 = 439 * 6047
2655337 = 503 * 5279
2657113 = 839 * 3167
2657177 = 863 * 3079
2657659 = 1151 * 2309
2657693 = 1187 * 2239
2657749 = 1259 * 2111
2657833 = 1439 * 1847
2657849 = 1511 * 1759
2661119 = 2661119

Q. Please send some more terms fo this sequence.