Question 97
For each positive integer $n$ larger than $1$ with prime factorization $p_1^{\alpha_1} p_2^{\alpha_2} \cdots p_k^{\alpha_k}$, its signature is defined as the sum $\alpha_1 + \alpha_2 + \cdots + \alpha_k$. Does there exist $2020$ consecutive positive integers such that among them, there are exactly $1812$ integers whose signatures are strictly smaller than $11$?