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A217261
Numbers of the form i^j^k, for i,j,k > 1.
2
16, 81, 256, 512, 625, 1296, 2401, 4096, 6561, 10000, 14641, 19683, 20736, 28561, 38416, 50625, 65536, 83521, 104976, 130321, 160000, 194481, 234256, 262144, 279841, 331776, 390625, 456976, 531441, 614656, 707281, 810000, 923521, 1048576, 1185921
OFFSET
1,1
COMMENTS
Also numbers of the form i^j^2, since i^j^k = (i^j^(k-2))^j^2.
LINKS
MATHEMATICA
t = {}; lim = 10^7; Do[n = i^j^k; If[n < lim, AppendTo[t, n]], {i, 2, lim^(1/4)}, {j, 2, Log[2, lim]}, {k, 2, Log[2, Log[2, lim]]}]; t = Union[t] (* T. D. Noe, Oct 01 2012 *)
PROG
(PARI) list(lim)=my(v=List()); for(i=2, (.5+lim\=1)^.25, for(j=2, sqrt(log(lim+.5)/log(i)), listput(v, i^j^2))); vecsort(Vec(v), , 8) \\ Charles R Greathouse IV, Oct 01 2012
(Haskell)
import Data.Set (singleton, insert, deleteFindMin)
a217261 n = a217261_list !! (n-1)
a217261_list = f [3..] $ singleton (16, (2, 2)) where
f xs'@(x:xs) s
| m > x ^ 4 = f xs $ insert (x ^ 4, (x, 2)) s
| m == x ^ 4 = f xs s
| otherwise = m : f xs' (insert (i ^ (j + 1) ^ 2, (i, j + 1)) s')
where ((m, (i, j)), s') = deleteFindMin s
-- Reinhard Zumkeller, Jun 29 2013
CROSSREFS
Sequence in context: A212898 A212145 A250362 * A372405 A277562 A217709
KEYWORD
nonn,nice
AUTHOR
STATUS
approved