%I #11 Jan 13 2021 11:26:43
%S 4,9,16,32,36,49,81,121,128,144,169,196,243,256,324,400,441,484,576,
%T 625,841,900,961,1024,1156,1225,1296,1369,1444,1521,1600,1681,1849,
%U 1936,2025,2048,2187,2209,2304,2401,2601,2704,2916,3025,3125,3249,3364,3600
%N Noncube perfect powers. [Warning: definition does not match the DATA.]
%C The NAME suggests that this is an erroneous version of A340585 (which includes 25, for example), but the Haskell implementation indicates that the true definition is more complicated. - _R. J. Mathar_, Jan 13 2021
%H Reinhard Zumkeller, <a href="/A239870/b239870.txt">Table of n, a(n) for n = 1..10000</a>
%F A052409(a(n)) mod 3 > 0.
%o (Haskell)
%o import Data.Map (singleton, findMin, deleteMin, insert)
%o a239870 n = a239870_list !! (n-1)
%o a239870_list = f 9 (3, 2) (singleton 4 (2, 2)) where
%o f zz (bz, ez) m
%o | xx < zz = if ex `mod` 3 > 0
%o then xx : f zz (bz, ez+1) (insert (bx*xx) (bx, ex+1) $ deleteMin m)
%o else f zz (bz, ez+1) (insert (bx*xx) (bx, ex+1) $ deleteMin m)
%o | xx > zz = if ez `mod` 3 > 0
%o then zz : f (zz+2*bz+1) (bz+1, 2) (insert (bz*zz) (bz, 3) m)
%o else f (zz+2*bz+1) (bz+1, 2) (insert (bz*zz) (bz, 3) m)
%o | otherwise = f (zz+2*bz+1) (bz+1, 2) m
%o where (xx, (bx, ex)) = findMin m -- bx ^ ex == xx
%Y Cf. A097054, A239728, intersection of A007412 and A001597.
%K nonn,obsc
%O 1,1
%A _Reinhard Zumkeller_, Mar 28 2014