12. If a natural number can be written as the sum of several consecutive natural numbers, then this natural number is called a "lonely number", for example, 4 is a "lonely number", but 6 is not. Then, among the natural numbers less than 2021, there are $\qquad$ "lonely numbers".
【Answer】10
【Analysis】Let the smallest of the consecutive natural numbers be $a$, with a total of $k$ terms, $k>1, S=a+(a+1)+\cdots+(a+k-1)$. $S=\frac{k(2 a+k-1)}{2}$, so $2 S=k(2 a+k-1)$.
Here, $2 a+k-1$ and $k$ are one odd and one even, and when $a$ is not equal to 0, $2 a+k-1>k$. When $S=2^{x}$, $2 S=2^{x+1}=k(2 a+k-1), 2^{x+1}$ has only one odd factor $1, k=1$ or $2 a+k-1=1$.
(1) When $k=1$, it contradicts the problem statement. (2) When $2 a+k-1=1$, $k=2^{x+1}, x$ and $a$ are both 0, which holds true.
(2) When $S=2^{x} \times P, P$ is an odd number not equal to 1, $2^{x+1} \times P=k(2 a+k-1)$.

We can let $k=2^{x-1}, P=2 a+k-1$ or $2 a+k-1=2^{x-1}, k=P$
In both cases, $a$ can definitely be solved, meaning such $S$ are not “lonely numbers”.
$S=2^{x}, x$ not equal to 0, and $S$ less than 2021, the natural numbers are $2^{1}$ to $2^{10}$, a total of 10.
$P S$ : If a natural number $N$ has $k$ odd divisors greater than 1, then $N$ has $k$ ways to be expressed as the sum of two or more consecutive positive integers.