Yes, it turns out that the answer is Googlable... I like to call these "factorially self-referential" numbers, in that they refer to their own prime factors:
14 = 1st prime x 4th prime
154 = 1st prime x 5th prime x 4th prime
1196 = 1st x 1st x 9th x 6th
2127 = 2nd x 127th
61411 = 61st x 4th x 11th
66079 = 6th x 6th x 7th x 9th
172482 = 1st x 7th x 24th x 8th x 2nd
223227 = 2nd x 232nd x 2nd x 7th
279174 = 2nd x 7th x 9th x 1st x 7th x 4th
291318 = 2nd x 9th x 1st x 318th
I think this is it for integers below 1 million. Perhaps others will want to look for more -- or just let this bit of silliness stop...