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A239870 Noncube perfect powers. [Warning: definition does not match the DATA.].

%I A239870 #13 Jul 23 2025 11:01:05
%S A239870 4,9,16,32,36,49,81,121,128,144,169,196,243,256,324,400,441,484,576,
%T A239870 625,841,900,961,1024,1156,1225,1296,1369,1444,1521,1600,1681,1849,
%U A239870 1936,2025,2048,2187,2209,2304,2401,2601,2704,2916,3025,3125,3249,3364,3600
%N A239870 Noncube perfect powers. [Warning: definition does not match the DATA.].
%C A239870 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 A239870 Reinhard Zumkeller, <a href="/A239870/b239870.txt">Table of n, a(n) for n = 1..10000</a>
%F A239870 A052409(a(n)) mod 3 > 0.
%o A239870 (Haskell)
%o A239870 import Data.Map (singleton, findMin, deleteMin, insert)
%o A239870 a239870 n = a239870_list !! (n-1)
%o A239870 a239870_list = f 9 (3, 2) (singleton 4 (2, 2)) where
%o A239870    f zz (bz, ez) m
%o A239870     | xx < zz = if ex `mod` 3 > 0
%o A239870       then xx : f zz (bz, ez+1) (insert (bx*xx) (bx, ex+1) $ deleteMin m)
%o A239870       else      f zz (bz, ez+1) (insert (bx*xx) (bx, ex+1) $ deleteMin m)
%o A239870     | xx > zz = if ez `mod` 3 > 0
%o A239870       then zz : f (zz+2*bz+1) (bz+1, 2) (insert (bz*zz) (bz, 3) m)
%o A239870       else      f (zz+2*bz+1) (bz+1, 2) (insert (bz*zz) (bz, 3) m)
%o A239870     | otherwise = f (zz+2*bz+1) (bz+1, 2) m
%o A239870     where (xx, (bx, ex)) = findMin m  --  bx ^ ex == xx
%Y A239870 Cf. A097054, A239728, intersection of A007412 and A001597.
%K A239870 nonn,obsc
%O A239870 1,1
%A A239870 _Reinhard Zumkeller_, Mar 28 2014