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A226777 Higher powers that are sums of two distinct higher powers.

%I A226777 #21 Feb 14 2018 04:02:29
%S A226777 243,2744,6561,177147,185193,474552,614656,810000,941192,1124864,
%T A226777 1419857,1500625,3241792,4782969,7962624,11239424,16003008,17850625,
%U A226777 21952000,26873856,28372625,52200625,68574961,82312875,117649000,129140163,162771336,200201625,238328000
%N A226777 Higher powers that are sums of two distinct higher powers.
%C A226777 x is in the sequence iff there are distinct y,z such that x = y + z and x,y,z are all in A076467.
%H A226777 Robert Israel and Reinhard Zumkeller, <a href="/A226777/b226777.txt">Table of n, a(n) for n = 1..1000</a> (first 264 terms from Robert Israel)
%e A226777 243 is in the sequence because 243 = 3^5 = 3^3 + 6^3.
%p A226777 N :=  10^12: # to get terms up to N
%p A226777 S := {seq(seq(a^x, a=1 .. floor(N^(1/x))), x = 3 .. floor(log[2](N)))}:
%p A226777 f:= proc(n) local L; L:= S[1..n-1] minus {S[n]/2}; nops(map2(`-`,S[n],L) intersect L) > 0 end proc;
%p A226777 A:= map(t -> S[t], select(f,[$1..nops(S)]));
%t A226777 max = 3*10^8; pp = Join[{1}, Table[n^k, {k, 3, Floor[Log[2, max]]}, {n, 2, Floor[max^(1/k)]}] // Flatten // Union]; Select[Total /@ Subsets[pp, {2}], MemberQ[pp, #]&] // Union (* _Jean-François Alcover_, Feb 14 2018 *)
%o A226777 (Haskell)
%o A226777 import qualified Data.Set as Set (null, split, filter)
%o A226777 import Data.Set (Set, empty, insert, member)
%o A226777 a226777 n = a226777_list !! (n-1)
%o A226777 a226777_list = f a076467_list empty where
%o A226777    f (x:xs) s | Set.null $ Set.filter ((`member` s) . (x -)) s'
%o A226777                           = f xs (x `insert` s)
%o A226777               | otherwise = x : f xs (x `insert` s)
%o A226777               where (s', _) = Set.split (x `div` 2) s
%o A226777 -- _Reinhard Zumkeller_, Sep 13, Jun 19 2013
%K A226777 nonn
%O A226777 1,1
%A A226777 _Robert Israel_, Jun 17 2013