Find all Super Powers
Ruby, 97 93 characters

puts (r=2..32).map{|j|r.map{|i|(1..2**(64.0/j/i)).map{|a|a**(j*i)}}}.flatten.uniq.sort[0..-2]


I'm pretty sure this should be correct.

$ time ruby1.9 perfectpower.rb &gt; out

real    0m0.199s
user    0m0.160s
sys     0m0.030s

$ wc -l out
67385 out

$ head -6 out
1
16
64
81
256
512

$ tail -3 out
18443366605910179921
18444492376972984336
18445618199572250625