A274245 Numbers n such that n*(n+1)/2 is a Taxi-cab number (A001235).

349999, 591408, 405332018, 525796270

Offset: 1

Author

Altug Alkan, Jul 02 2016

Keywords

• nonn
• more

Comments

In other words, numbers n such that 0 + 1 + 2 + ... + n = a^3 + b^3 = c^3 + d^3 where (a, b) and (c, d) are distinct pairs and a, b, c, d > 0 is soluble.

It is known that there is no triangular number that is also a cube except 0 and 1. So if the sum of k positive cubes is a triangular number that is bigger than 1, then the minimum value of k is 2. At this point sequence focuses on that question: What are the triangular numbers that are the sum of two positive cubes in more than one way?

A000217(349999) = 61249825000 is the least triangular number that is also a Taxi-cab number.

a(5) > 10^9. - Giovanni Resta, Jul 04 2016

Examples

			349999 is a term because 349999*(349999+1) / 2 = 61249825000 = 820^3 + 3930^3 = 3018^3 + 3232^3.
591408 is a term because 591408*(591408+1) / 2 = 174882006936 = 2070^3 + 5496^3 = 3238^3 + 5204^3.
		

Crossrefs

Cf. A000217, A001235.

Extensions

a(3)-a(4) from Giovanni Resta, Jul 04 2016