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A076468
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Perfect powers m^k where k >= 4.
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4
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1, 16, 32, 64, 81, 128, 243, 256, 512, 625, 729, 1024, 1296, 2048, 2187, 2401, 3125, 4096, 6561, 7776, 8192, 10000, 14641, 15625, 16384, 16807, 19683, 20736, 28561, 32768, 38416, 46656, 50625, 59049, 65536, 78125, 83521, 100000, 104976, 117649
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OFFSET
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1,2
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COMMENTS
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If p|n then at least p^4|n.
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LINKS
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FORMULA
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Sum_{n>=1} 1/a(n) = 3 - zeta(2) - zeta(3) + Sum_{k>=2} mu(k)*(3 - zeta(k) - zeta(2*k) - zeta(3*k)) = 1.1473274274... . - Amiram Eldar, Dec 03 2022
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MATHEMATICA
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a = {1}; Do[ If[ Apply[ GCD, Last[ Transpose[ FactorInteger[n]]]] > 3, a = Append[a, n]; Print[n]], {n, 2, 131071}]; a
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PROG
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(Haskell)
import qualified Data.Set as Set (null)
import Data.Set (empty, insert, deleteFindMin)
a076468 n = a076468_list !! (n-1)
a076468_list = 1 : f [2..] empty where
f xs'@(x:xs) s | Set.null s || m > x ^ 4 = f xs $ insert (x ^ 4, x) s
| m == x ^ 4 = f xs s
| otherwise = m : f xs' (insert (m * b, b) s')
where ((m, b), s') = deleteFindMin s
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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