Numerator sixty

\[\frac{60}{61},\ \frac{60}{67},\ \frac{60}{71},\ \ldots\]

How many reduced positive fractions less than 1 are there with the numerator equal to 60 and the denominators less than 10,000?

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Clarification:

  • The fraction \(\frac{60}{122}\) does not count because it can be reduced to \(\frac{30}{61}\).
  • The fractions \(\frac{60}3\) and \(\frac{60}{60}\) do not count because they are not less than 1.
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