A085332 -id:A085332 - cp's OEIS frontend

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

Altug Alkan, Jan 10 2016

nonn

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.

			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.

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

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

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, ", ")))

A085333 a(n) is the least n-th power of a prime that is the sum of two positive cubes, or 0 if no solution exists (for n=3k).

Original entry on oeis.org

2, 9, 0, 16, 243, 0, 128, 6561, 0, 1024, 177147, 0, 8192, 4782969, 0, 65536, 129140163, 0, 524288, 3486784401, 0, 4194304, 94143178827, 0, 33554432, 2541865828329, 0, 268435456, 68630377364883, 0, 2147483648, 1853020188851841, 0

Offset: 1

Labos Elemer, Jul 07 2003

nonn

Cf. A085332.

a(n) is the least solution to p^n=x^3+y^3, x, y>0 or a(n)=a(3k)=0 labels cases if no solution exists.
a(3k)=0, a(3k+1)=2^(3k+1), a(3k+2)=3^(3k+2).
From Chai Wah Wu, May 18 2017: (Start)
a(n) = 35*a(n-3) - 216*a(n-6) for n > 6.
G.f.: x*(-72*x^4 - 54*x^3 + 9*x + 2)/(216*x^6 - 35*x^3 + 1). (End)

Formula, corrected description and more terms from Ray Chandler, Jul 20 2003

cp's OEIS Frontend

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

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A085333 a(n) is the least n-th power of a prime that is the sum of two positive cubes, or 0 if no solution exists (for n=3k).

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