BG-MO 2012 Problem 1

The sequence $a_1,a_2,a_3\ldots$ , consisting of natural numbers, is defined by the rule: $$a_{n+1}=a_{n}+2t(n)$$ for every natural number $n$ , where $t(n)$ is the number of the different divisors of $n$ (including $1$ and $n$ ). Is it possible that two consecutive members of the sequence are squares of natural numbers?