1992 AIME Problem 5

Let S^{}_{} be the set of all rational numbers r^{}_{}, 0^{}_{}<r<1, that have a repeating decimal expansion in the form 0.abcabcabc\ldots=0.\overline{abc}, where the digits a^{}_{}, b^{}_{}, and c^{}_{} are not necessarily distinct. To write the elements of S^{}_{} as fractions in lowest terms, how many different numerators are required?

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.