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In my previous MO question (see here), I solved the case for arithmetic progressions $f_k(x)=q_k x+1$. The solution is this: The list of sequences $f_k(x)$, each one corresponding to a specific $k$, ...

A Bogotá number is a non-negative integer equal to some smaller number, or itself, times its digital product, i.e. the product of its digits. For example, 138 is a Bogotá number because 138 = 23 x (2 ...

We denote for integers $m>1$ the product of the distinct prime numbers dividing $m$ as $$\operatorname{rad}(m)=\prod_{\substack{p\mid m\\p\text{ prime}}}p,$$ with the definition $\operatorname{rad}(...