Question 113
Characterize all positive integers $n \gt 1$ for which the expression
$$
(n-1)! \cdot \left(1 + \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{n-1}\right)
$$
is not divisible by $n$.
$$
(n-1)! \cdot \left(1 + \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{n-1}\right)
$$
is not divisible by $n$.