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A239728
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Perfect power but neither square nor cube.
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5
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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)
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OFFSET
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1,1
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LINKS
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FORMULA
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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
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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