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

4, 9, 16, 32, 36, 49, 81, 121, 128, 144, 169, 196, 243, 256, 324, 400, 441, 484, 576, 625, 841, 900, 961, 1024, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1849, 1936, 2025, 2048, 2187, 2209, 2304, 2401, 2601, 2704, 2916, 3025, 3125, 3249, 3364, 3600

Offset: 1

Author

Reinhard Zumkeller, Mar 28 2014

Keywords

• nonn
• obsc

Comments

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A097054, A239728, intersection of A007412 and A001597.

Programs

Haskell

import Data.Map (singleton, findMin, deleteMin, insert)
a239870 n = a239870_list !! (n-1)
a239870_list = f 9 (3, 2) (singleton 4 (2, 2)) where
   f zz (bz, ez) m
    | xx < zz = if ex `mod` 3 > 0
      then xx : f zz (bz, ez+1) (insert (bx*xx) (bx, ex+1) $ deleteMin m)
      else      f zz (bz, ez+1) (insert (bx*xx) (bx, ex+1) $ deleteMin m)
    | xx > zz = if ez `mod` 3 > 0
      then zz : f (zz+2*bz+1) (bz+1, 2) (insert (bz*zz) (bz, 3) m)
      else      f (zz+2*bz+1) (bz+1, 2) (insert (bz*zz) (bz, 3) m)
    | otherwise = f (zz+2*bz+1) (bz+1, 2) m
    where (xx, (bx, ex)) = findMin m  --  bx ^ ex == xx

Formula

A052409(a(n)) mod 3 > 0.