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A267088 Perfect powers of the form x^3 + y^3 where x and y are positive integers.

%I A267088 #24 Oct 04 2017 01:08:51
%S A267088 9,16,128,243,576,1024,6561,8192,9604,11664,28224,36864,51984,65536,
%T A267088 97344,140625,177147,250000,275625,345744,419904,450241,524288,614656,
%U A267088 717409,746496,1028196,1058841,1399489,1500625,1590121,1750329,1806336,1882384,2359296,3326976,4194304
%N A267088 Perfect powers of the form x^3 + y^3 where x and y are positive integers.
%C A267088 Intersection of A001597 and A003325.
%C A267088 Motivation for this sequence is the equation m^k = x^3 + y^3 where x,y,m > 0 and k >= 2.
%C A267088 Obviously, because of Fermat's Last Theorem, a(n) cannot be a cube.
%C A267088 A050802 is a subsequence.
%C A267088 Obviously, this sequence contains all numbers of the form 2^(3*n+1) and 3^(3*n-1), for n > 0.
%H A267088 Chai Wah Wu, <a href="/A267088/b267088.txt">Table of n, a(n) for n = 1..5012</a>
%e A267088 9 is a term because 9 = 3^2 = 1^3 + 2^3.
%e A267088 16 is a term because 16 = 2^4 = 2^3 + 2^3.
%e A267088 243 is a term because 243 = 3^5 = 3^3 + 6^3.
%o A267088 (PARI) T = thueinit('z^3+1);
%o A267088 is(n) = #select(v->min(v[1], v[2])>0, thue(T, n))>0;
%o A267088 for(n=2, 1e7, if(ispower(n) && is(n), print1(n, ", ")))
%Y A267088 Cf. A001597, A003325, A050802, A085332, A013730, A013733, A266927.
%K A267088 nonn
%O A267088 1,1
%A A267088 _Altug Alkan_, Jan 10 2016