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).

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

Author

Labos Elemer, Jul 07 2003

Keywords

• nonn

Crossrefs

Cf. A085332.

Formula

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)

Extensions

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