Give the smallest number that has N divisors
APL, 25 24 23 characters
f←{({+/⍵=⍵∧⍳⍵}¨⍳2*⍵)⍳⍵}

Defines a function f which can then be used to calculate the numbers:
&gt; f 13
4096

&gt; f 14
192

The solution utilizes the fact that LCM(n,x)==n iff x divides n. Thus, the block {+/⍵=⍵∧⍳⍵} simply calculates the number of divisors. This function is applied to all numbers from 1 to 2^d ¨⍳2*⍵. The resulting list is then searched for d itself (⍳⍵) which is the desired function f(d).