Jeffie Foodlemyer needs to hire an accountant. Three people apply for the job. He decides to use a mathematical puzzle to test each accountant's numeric skills. He chooses 4 integers greater than 1, and tells the first applicant their product. The accountant immediately tells him the 4 numbers. Too easy.

He tells the second applicant the sum of the squares of the 4 numbers. Again, the accountant tells him the 4 numbers immediately. Still too easy.

So he tells the last applicant the product of the 3 smallest numbers plus twice the square of the largest number. That accountant is unable to tell him the 4 numbers. Note that, he interviews the 3 accountants separately.

What 4 numbers did he choose?