We say that a number is [i]superstitious [/i] when it is equal to $13$ times the sum of its digits . Find all superstitious numbers.
1. **Define the problem**: We need to find all numbers that are equal to 13 times the sum of their digits. We call such numbers *superstitious*.

2. **Consider two-digit numbers**: Let the two-digit number be represented as \(10a + b\), where \(a\) and \(b\) are the digits.
   \[
   10a + b = 13(a + b)
   \]
   Simplify the equation:
   \[
   10a + b = 13a + 13b
   \]
   \[
   10a + b - 13a - 13b = 0
   \]
   \[
   -3a - 12b = 0
   \]
   \[
   a + 4b = 0
   \]
   Since \(a\) and \(b\) are digits (0-9), there are no non-negative integer solutions for \(a\) and \(b\) that satisfy this equation. Therefore, there are no two-digit superstitious numbers.

3. **Consider three-digit numbers**: Let the three-digit number be represented as \(100a + 10b + c\), where \(a\), \(b\), and \(c\) are the digits.
   \[
   100a + 10b + c = 13(a + b + c)
   \]
   Simplify the equation:
   \[
   100a + 10b + c = 13a + 13b + 13c
   \]
   \[
   100a + 10b + c - 13a - 13b - 13c = 0
   \]
   \[
   87a - 3b - 12c = 0
   \]
   \[
   29a = b + 4c
   \]
   Since \(a\), \(b\), and \(c\) are digits (0-9), we need to find values that satisfy this equation. 

4. **Solve for \(a = 1\)**: 
   \[
   29 \cdot 1 = b + 4c
   \]
   \[
   29 = b + 4c
   \]
   We need to find \(b\) and \(c\) such that this equation holds:
   - If \(c = 7\), then \(b = 29 - 4 \cdot 7 = 29 - 28 = 1\). This gives the number \(100 \cdot 1 + 10 \cdot 1 + 7 = 117\).
   - If \(c = 6\), then \(b = 29 - 4 \cdot 6 = 29 - 24 = 5\). This gives the number \(100 \cdot 1 + 10 \cdot 5 + 6 = 156\).
   - If \(c = 5\), then \(b = 29 - 4 \cdot 5 = 29 - 20 = 9\). This gives the number \(100 \cdot 1 + 10 \cdot 9 + 5 = 195\).

5. **Verify the solutions**: 
   - For \(117\):
     \[
     1 + 1 + 7 = 9 \quad \text{and} \quad 13 \cdot 9 = 117
     \]
   - For \(156\):
     \[
     1 + 5 + 6 = 12 \quad \text{and} \quad 13 \cdot 12 = 156
     \]
   - For \(195\):
     \[
     1 + 9 + 5 = 15 \quad \text{and} \quad 13 \cdot 15 = 195
     \]

Thus, the three-digit superstitious numbers are \(117\), \(156\), and \(195\).

The final answer is \(\boxed{117, 156, 195}\).