Sort the unique numbers in a multiplication table

Python 2, 61 51 bytes

lambda n:sorted({~(i%n)*~(i/n)for i in range(n*n)})

Thanks to xnor for shortening some syntax.

Pyth, 8 bytes

S{*M^SQ2

Try it online.

Explanation: SQ takes the evaluated list input (Q) and makes a list [1, 2, ..., Q]. ^SQ2 takes the Cartesian product of that list with itself - all possible product combinations. *M multiplies all these pairs together to form all possible results in the multiplication table and S{ makes it unique and sorts it.

APL, 18 16 bytes

{y[⍋y←∪,∘.×⍨⍳⍵]}

This is an unnamed monadic function. The output is in ascending order.

Explanation:

             ⍳⍵]}   ⍝ Get the integers from 1 to the input
         ∘.×⍨       ⍝ Compute the outer product of this with itself
        ,           ⍝ Flatten into an array
       ∪            ⍝ Select unique elements
     y←             ⍝ Assign to y
 {y[⍋               ⍝ Sort ascending

Fixed an issue and saved 2 bytes thanks to Thomas Kwa!