14.5.3 * Express the natural number $n$ as the sum of as many distinct natural numbers as possible. Find the maximum possible number of summands.

Express the natural number $n$ as the sum of as many distinct natural numbers as possible. Find the maximum possible number of summands.
For $n$, there exists $k$ such that $\frac{1}{2} k(k+1)=1+2+3+\cdots+k \leqslant n<1+2+\cdots+k+(k+1)$. From the problem, we know that $k$ is the maximum number, at this time $k \leqslant \frac{1}{2}(\sqrt{8 n+1}-1)$, thus $k=$ $\left[\frac{1}{2}(\sqrt{8 n+1}-1)\right]$