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A239728 Perfect power but neither square nor cube. 5
32, 128, 243, 2048, 2187, 3125, 7776, 8192, 16807, 78125, 100000, 131072, 161051, 177147, 248832, 279936, 371293, 524288, 537824, 759375, 823543, 1419857, 1594323, 1889568, 2476099, 3200000, 4084101, 5153632, 6436343, 7962624, 8388608, 10000000, 11881376, 17210368 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

FORMULA

GCD(A052409(a(n), 6) = 1. - Reinhard Zumkeller, Mar 28 2014

Sum_{n>=1} 1/a(n) = 1 - zeta(2) - zeta(3) + zeta(6) + Sum_{k>=2} mu(k)*(1-zeta(k)) = 0.0448164603... - Amiram Eldar, Dec 21 2020

EXAMPLE

279936 is included since 279936 = 6^7 is a power and this is not a square or a cube.

59049 = 9^5 not included since this is a square 243^2 = 59049.

32768 = 8^5 not included since this is a cube 32^3 = 32768.

PROG

(PARI) for(i=1, 2^25, if(gcd(ispower(i), 6) == 1, print(i)))

(Haskell)

import Data.Map (singleton, findMin, deleteMin, insert)

a239728 n = a239728_list !! (n-1)

a239728_list = f 9 (3, 2) (singleton 4 (2, 2)) where

   f zz (bz, be) m

    | xx < zz && gcd 6 be > 1 =

                f zz (bz, be+1) (insert (bx*xx) (bx, be+1) $ deleteMin m)

    | xx < zz = xx :

                f zz (bz, be+1) (insert (bx*xx) (bx, be+1) $ deleteMin m)

    | xx > zz = 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, be)) = findMin m

-- Reinhard Zumkeller, Mar 28 2014

CROSSREFS

Cf. A001597 (perfect powers), A097054 (nonsquare perfect powers),  A239870 (noncube perfect powers).

Cf. A008683, A052409.

Sequence in context: A271532 A264480 A247155 * A244082 A033323 A091905

Adjacent sequences:  A239725 A239726 A239727 * A239729 A239730 A239731

KEYWORD

nonn,easy

AUTHOR

Jeppe Stig Nielsen, Mar 25 2014

STATUS

approved

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Last modified March 2 09:56 EST 2021. Contains 341746 sequences. (Running on oeis4.)