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Noncube perfect powers. [Warning: definition does not match the DATA.]
5

%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