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

1,1

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.

Links

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

Example

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.

Prog

(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, ", ")))

Crossrefs

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

Sequence in context: A138238 A177171 A226232 * A204268 A075373 A072470

Adjacent sequences: A267085 A267086 A267087 * A267089 A267090 A267091

Keyword

nonn

Author

Altug Alkan, Jan 10 2016

Status

approved