Question 23
Let $h_n$ and $k_n$ be the unique relatively prime positive integers such that
$$
\frac11+\frac12+\frac13+\cdots+\frac1n=\frac{h_n}{k_n}.
$$
Let $L_n$ denote the least common multiple of the numbers $1,$ $2,$ $3,$ $\ldots,$ $n.$ For how many integers $n$ with $1\le n\le22$ is $k_n\lt L_n?$
$$
\frac11+\frac12+\frac13+\cdots+\frac1n=\frac{h_n}{k_n}.
$$
Let $L_n$ denote the least common multiple of the numbers $1,$ $2,$ $3,$ $\ldots,$ $n.$ For how many integers $n$ with $1\le n\le22$ is $k_n\lt L_n?$