Factorize it! ...badly
CJam - 66

ria{_{:XmF{1=1&gt;},La\{a1$\f++}/La-{XI{~#}%:*/I{si}%:**}fI}%|}1e3*$p


Try it at http://cjam.aditsu.net/

Explanation:

ria                       read token, convert to integer and wrap in array
{…}1e3*                   repeat 1000 times
    _                     duplicate array
    {…}%                  transform each array item (number) using the block
        :X                store the number in X
        mF                factorize with exponents
        {1=1&gt;},           keep only the factors with exponent &gt; 1
        La\{a1$\f++}/     get all the subsets (*)
        La-               remove the empty subset
        {…}fI             for I = each subset of prime factors with exponent &gt; 1
            XI{~#}%:*/    divide X by all the factors in I
            I{si}%:**     multiply with the primes from I
                          concatenated with their exponents
    |                     add the new numbers to the array, removing duplicates
$                         sort
p                         print the final array


(*) Thanks Martin