OFFSET
1,1
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
EXAMPLE
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
KEYWORD
nonn,more
AUTHOR
Altug Alkan, Jul 02 2016
EXTENSIONS
a(3)-a(4) from Giovanni Resta, Jul 04 2016
STATUS
approved