MathNet 2007-part-01 — 187 problems (EN–VI) Question 106

For every positive integer $n$ set $a_n = 0$, if the number of divisors of $n$, greater than $2007$, is even and $a_n = 1$, if this number is odd. Is the number $\alpha = 0, a_1a_2a_3 \dots a_k \dots$ rational?