The number $2$ has the interesting property that whenever $n>1$ is an integer, then $n \nmid (2^n-1)$. (It's a good exercise to prove this statement.)

Let's call a positive integer $2$-like if for all integers $n>1$ we have $n\nmid (b^n-1)$, and let's call it almost $2$-like if for all integers $n>1$ except finitely many we have $n\nmid (b^n-1)$.

Question. Is the collection of almost $2$-like numbers a proper superset of the collection of $2$-like numbers?

The number $2$ has the interesting property that whenever $n>1$ is an integer, then $n \nmid (2^n-1)$. (It's a good exercise to prove this statement.)

Let's call a positive integer $b$ $2$-like if for all integers $n>1$ we have $n\nmid (b^n-1)$, and let's call it almost $2$-like if for all integers $n>1$ except finitely many we have $n\nmid (b^n-1)$.

Question. Is the collection of almost $2$-like numbers a proper superset of the collection of $2$-like numbers?