Question 154
Let us denote by $deg(n) = \alpha_1 + \alpha_2 + \ldots + \alpha_k$ the degree of the number $n = p_1^{\alpha_1} p_2^{\alpha_2} \ldots p_k^{\alpha_k}$, where $p_i$ are pairwise different prime numbers, and $\alpha_1, \alpha_2, \ldots, \alpha_k$ are positive integers. Prove that there exist $2016$ consecutive positive integers among which there are precisely $1000$ numbers with the degree less than $11$.
(Bogdan Kivva)
(Bogdan Kivva)