Question 52
Find all strictly increasing sequences $(a_n)_n$ of positive integers with the following two properties:
a) $a_1^3 + a_2^3 + \dots + a_n^3 = (a_1 + a_2 + \dots + a_n)^2$, for every integer $n \ge 2014$;
b) for every integer $k \ge 2015$, the number $a_1 + a_2 + \dots + a_{2014}$ cannot be written as a sum of $k$ consecutive positive integers.
a) $a_1^3 + a_2^3 + \dots + a_n^3 = (a_1 + a_2 + \dots + a_n)^2$, for every integer $n \ge 2014$;
b) for every integer $k \ge 2015$, the number $a_1 + a_2 + \dots + a_{2014}$ cannot be written as a sum of $k$ consecutive positive integers.