cp's OEIS Frontend

A217261 Numbers of the form i^j^k, for i,j,k > 1.

%I A217261 #19 May 07 2025 19:58:39
%S A217261 16,81,256,512,625,1296,2401,4096,6561,10000,14641,19683,20736,28561,
%T A217261 38416,50625,65536,83521,104976,130321,160000,194481,234256,262144,
%U A217261 279841,331776,390625,456976,531441,614656,707281,810000,923521,1048576,1185921,1336336,1500625,1679616,1874161,1953125
%N A217261 Numbers of the form i^j^k, for i,j,k > 1.
%C A217261 Also numbers of the form i^j^2, since i^j^k = (i^j^(k-2))^j^2.
%H A217261 Reinhard Zumkeller, <a href="/A217261/b217261.txt">Table of n, a(n) for n = 1..10000</a>
%t A217261 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 *)
%t A217261 Select[Union[Flatten[Table[i^j^2,{i,2,50},{j,2,50}]]],#<12*10^5&] (* _Harvey P. Dale_, Jan 15 2025 *)
%o A217261 (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
%o A217261 (Haskell)
%o A217261 import Data.Set (singleton, insert, deleteFindMin)
%o A217261 a217261 n = a217261_list !! (n-1)
%o A217261 a217261_list = f [3..] $ singleton (16, (2, 2)) where
%o A217261    f xs'@(x:xs) s
%o A217261      | m > x ^ 4  = f xs $ insert (x ^ 4, (x, 2)) s
%o A217261      | m == x ^ 4 = f xs s
%o A217261      | otherwise  = m : f xs' (insert (i ^ (j + 1) ^ 2, (i, j + 1)) s')
%o A217261      where ((m, (i,j)), s') = deleteFindMin s
%o A217261 -- _Reinhard Zumkeller_, Jun 29 2013
%o A217261 (Python)
%o A217261 def generate(limit: int) -> list:
%o A217261     numbers = set()
%o A217261     # For very large range this list must be expanded:
%o A217261     for n in [2, 3, 5, 7]:
%o A217261         m = 2
%o A217261         j = n * n
%o A217261         while m**j <= limit:
%o A217261             numbers.add(m**j)
%o A217261             m += 1
%o A217261     return sorted(numbers)
%o A217261 A217261List = generate(2000000)
%o A217261 print(A217261List)  # _Peter Luschny_, May 07 2025
%K A217261 nonn,nice
%O A217261 1,1
%A A217261 _Franklin T. Adams-Watters_, Sep 28 2012