Awesome Fractions

\[\frac{17820}{495} = 36\]

The above is called an “awesome fraction” because it equals a positive integer and uses each of the digits 0 through 9 exactly once on either side of the equal sign (\(=\)).

What is the sum of all integers that can be expressed as awesome fractions?

Note: All integers must be expressed without leading zeros. You may make use of the coding environment below:


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