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

243, 2744, 6561, 177147, 185193, 474552, 614656, 810000, 941192, 1124864, 1419857, 1500625, 3241792, 4782969, 7962624, 11239424, 16003008, 17850625, 21952000, 26873856, 28372625, 52200625, 68574961, 82312875, 117649000, 129140163, 162771336, 200201625, 238328000

Offset: 1

Author

Robert Israel, Jun 17 2013

Keywords

• nonn

Comments

x is in the sequence iff there are distinct y,z such that x = y + z and x,y,z are all in A076467.

Examples

			243 is in the sequence because 243 = 3^5 = 3^3 + 6^3.
		

Links

• Robert Israel and Reinhard Zumkeller, Table of n, a(n) for n = 1..1000 (first 264 terms from Robert Israel)

Programs

Haskell

import qualified Data.Set as Set (null, split, filter)
import Data.Set (Set, empty, insert, member)
a226777 n = a226777_list !! (n-1)
a226777_list = f a076467_list empty where
   f (x:xs) s | Set.null $ Set.filter ((`member` s) . (x -)) s'
                          = f xs (x `insert` s)
              | otherwise = x : f xs (x `insert` s)
              where (s', _) = Set.split (x `div` 2) s
-- Reinhard Zumkeller, Sep 13, Jun 19 2013

Maple

N :=  10^12: # to get terms up to N
S := {seq(seq(a^x, a=1 .. floor(N^(1/x))), x = 3 .. floor(log[2](N)))}:
f:= proc(n) local L; L:= S[1..n-1] minus {S[n]/2}; nops(map2(`-`,S[n],L) intersect L) > 0 end proc;
A:= map(t -> S[t], select(f,[$1..nops(S)]));

Mathematica

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 *)