A274578 Nonsquare k such that k^3 - 1 is the average of two positive cubes.

2305, 2629, 4117, 7060, 37444, 46081, 113320, 208545, 449569, 474553, 507325, 1224757, 1499068, 1927405, 1931077, 2263129, 2350909, 2447596, 3107841, 4065517, 4274932, 4303321, 5646685, 6582865, 7225597, 10386273, 18432001, 21936709, 24218425, 24362989, 27351417

Offset: 1

Author

Altug Alkan, Jun 29 2016

Keywords

• nonn

Comments

The equation x^3 + y^3 = 2*z^3 has no integer solution triple (x, y, z) for x > y and z is nonzero. So this sequence focuses on the equation x^3 + y^3 = 2*(z^3 - 1) where x, y > 0.

Examples

			2305 is a term because it is not a square and 2305^3 - 1 = (144^3 + 2904^3) / 2.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..66

Crossrefs

Cf. A000037, A003325, A068601, A273822.

Programs

PARI

isA003325(n) = for(k=1, sqrtnint(n\2, 3), ispower(n-k^3, 3) && return(1));
lista(nn) = for(n=1, nn, if(isA003325(2*(n^3-1)) && !issquare(n), print1(n, ", ")));

Extensions

a(9)-a(25) from Chai Wah Wu, Aug 07 2020

a(26)-a(31) from Chai Wah Wu, Jun 30 2025