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

9, 16, 128, 243, 576, 1024, 6561, 8192, 9604, 11664, 28224, 36864, 51984, 65536, 97344, 140625, 177147, 250000, 275625, 345744, 419904, 450241, 524288, 614656, 717409, 746496, 1028196, 1058841, 1399489, 1500625, 1590121, 1750329, 1806336, 1882384, 2359296, 3326976, 4194304

Offset: 1

Author

Altug Alkan, Jan 10 2016

Keywords

• nonn

Comments

Intersection of A001597 and A003325.

Motivation for this sequence is the equation m^k = x^3 + y^3 where x,y,m > 0 and k >= 2.

Obviously, because of Fermat's Last Theorem, a(n) cannot be a cube.

A050802 is a subsequence.

Obviously, this sequence contains all numbers of the form 2^(3*n+1) and 3^(3*n-1), for n > 0.

Examples

			9 is a term because 9 = 3^2 = 1^3 + 2^3.
16 is a term because 16 = 2^4 = 2^3 + 2^3.
243 is a term because 243 = 3^5 = 3^3 + 6^3.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..5012

Crossrefs

Cf. A001597, A003325, A050802, A085332, A013730, A013733, A266927.

Programs

PARI

T = thueinit('z^3+1);
is(n) = #select(v->min(v[1], v[2])>0, thue(T, n))>0;
for(n=2, 1e7, if(ispower(n) && is(n), print1(n, ", ")))