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 A097054 Nonsquare perfect powers. 10
 8, 27, 32, 125, 128, 216, 243, 343, 512, 1000, 1331, 1728, 2048, 2187, 2197, 2744, 3125, 3375, 4913, 5832, 6859, 7776, 8000, 8192, 9261, 10648, 12167, 13824, 16807, 17576, 19683, 21952, 24389, 27000, 29791, 32768, 35937, 39304, 42875, 50653 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Terms of A001597 that are not in A000290. All terms of this sequence are also in A070265 (odd powers), but omitting those odd powers that are also a square (e.g. 64=4^3=8^2). LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Perfect Power. Eric Weisstein's World of Mathematics, Odd Power. FORMULA A052409(a(n)) is odd. - Reinhard Zumkeller, Mar 28 2014 Sum_{n>=1} 1/a(n) = 1 - zeta(2) + Sum_{k>=2} mu(k)*(1-zeta(k)) = 0.2295303015... - Amiram Eldar, Dec 21 2020 MAPLE # uses code of A001597 for n from 4 do     if not issqr(n) and isA001597(n) then         printf("%d, \n", n);     end if; end do: # R. J. Mathar, Jan 13 2021 MATHEMATICA nn = 50653; Select[Union[Flatten[Table[n^i, {i, Prime[Range[2, PrimePi[Log[2, nn]]]]}, {n, 2, nn^(1/i)}]]], ! IntegerQ[Sqrt[#]] &] (* T. D. Noe, Apr 19 2011 *) PROG (Haskell) import Data.Map (singleton, findMin, deleteMin, insert) a097054 n = a097054_list !! (n-1) a097054_list = f 9 (3, 2) (singleton 4 (2, 2)) where    f zz (bz, be) m     | xx < zz && even be =                 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 (PARI) is(n)=ispower(n)%2 \\ Charles R Greathouse IV, Aug 28 2016 CROSSREFS Cf. A001597 (perfect powers), A000290 (the squares), A008683, A070265 (odd powers), A097055, A097056, A239870, A239728, A093771. Sequence in context: A116002 A339595 A335988 * A304291 A056824 A297868 Adjacent sequences:  A097051 A097052 A097053 * A097055 A097056 A097057 KEYWORD nonn AUTHOR Hugo Pfoertner, Jul 21 2004 STATUS approved

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Last modified April 16 05:26 EDT 2021. Contains 343030 sequences. (Running on oeis4.)