A271717 Integers k such that both k and k^3-1 are the sum of two positive cubes (see A003325).

9, 11664, 36864, 38134, 345744, 1750329, 4782969, 20820969, 47775744, 65804544, 95004009, 150994944, 448084224, 733055625, 1093955625, 1416167424, 2197265625, 4318066944, 5194805625, 6198727824, 7169347584, 10771948944, 13013105625, 19591041024, 32427005625

Offset: 1

Author

Altug Alkan, Apr 12 2016

Keywords

• nonn

Comments

Values of a^3 + b^3 such that (a^3 + b^3)^3 - 1 is of the form x^3 + y^3 where a, b, x, y > 0.

38134 = 2*23*829 is the first term that is nonsquare. What are the next square terms of this sequence?

n is a member of A007412 and n^3 is a member of A003072, obviously.

Examples

			9 is a term because 9 = 1^3 + 2^3 and 9^3 - 1 = 6^3 + 8^3.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..33

Crossrefs

Cf. A003325, A050787, A068601.

Programs

PARI

isA003325(n) = for(k=1, sqrtnint(n\2, 3), ispower(n-k^3, 3) && return(1));
for(n=1, 1e7, if(isA003325(n) && isA003325(n^3-1), print1(n, ", ")));

Extensions

a(8)-a(16) from Chai Wah Wu, Apr 17 2016

a(17)-a(25) from Chai Wah Wu, Jul 21 2025