A269839 Integers k such that the sum of the first k cubes (A000537) is the sum of 2 positive cubes.

2, 49, 4557, 13689, 18816, 86015, 159249, 226981, 1368912, 2112278, 25153757, 85184000

Offset: 1

Author

Altug Alkan, Mar 06 2016

Keywords

• nonn
• more

Comments

In other words, integers k such that (1+2+3+...+k)^2 = x^3 + y^3 where x and y are positive integers, is soluble.

Examples

			49 is a term because A000537(49) = 1^3 + 2^3 + ... + 48^3 + 49^3 = 1500625 = 70^3 + 105^3.
4557 is a term because A000537(4557) = 1^3 + 2^3 + ... + 4556^3 + 4557^3 = 107856595472409 = 11620^3 + 47369^3.
		

Crossrefs

Cf. A000537, A003325.

Programs

PARI

isA003325(n) = for(k=1, sqrtnint(n\2, 3), ispower(n-k^3, 3) && return(1));
for(n=0, 1e7, if(isA003325((n*(n+1)/2)^2), print1(n, ", ")));

Extensions

a(6)-a(10) from Chai Wah Wu, Mar 08 2016

a(11)-a(12) from Chai Wah Wu, Jun 30 2025