13. A composite number, not a multiple of 3, but the sum of all its divisors equals twice the number. The smallest such number is
【Analysis】Method 1: Enumeration, found to be 28
Method 2: Since $2=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{6}$, the first number that meets the condition of all divisors summing to twice the number is 6, but 6 is a multiple of 3, so it is discarded.
$2=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{7}+\frac{1}{14}+\frac{1}{28}$, thus, the second number that meets the condition of all divisors summing to twice the number is 28, which is not a multiple of 3, so the required number is 28

【Note】The number mentioned in the problem is known as a perfect number