How many arrays

You are given two integers $N$ and $X$. Count the number of distinct arrays of length **at most** $N$, whose LCM is equal to $X$. That is, find the number of arrays $A$ such that: - $1 \leq |A| \leq N$, where $|A|$ denotes the length of $A$; and - $\text{lcm}(A_1, A_2, A_3, \ldots, A_{|A|}) = X$ Two arrays $A$ and $B$ are considered different if: - $A$ and $B$ have different lengths; or - $A$