The characterization of sums of consecutive integers

Let $n$ be a natural number. We say that $n$ is a sum of consecutive integers if there exist integers $a$ and $k\geq 2$ such that

$$n=a+(a+1)+\cdots+(a+k-1).$$

Consecutive-sum conjecture. A natural number is a sum of consecutive integers if and only if it is not a power of $2$. This characterizes exactly which natural numbers admit a representation as a sum of two or more consecutive integers, a classical elementary number-theory problem. The source presents this as a conjecture arising from small examples; no resolution is supplied in the given text.