Factorials in Denominator

Consider the sequence \(a_n=\dfrac{1}{d}\), with \(n\geq1\) of fractions:

\[\dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{4},\cdots,\dfrac{1}{1000!}\]

where \(d\) is the \((n+1)\)th divisor of \(1000!\) in increasing order. There is exactly one term \(\dfrac{1}{d}\) for every \(d \mid 1000!\) with \(d>1\).

And obviously, each term in the sequence is a rational number, where the decimal expansion of a rational number always terminates after a finite number of digits or repeats a finite sequence of digits over and over.

Find the number of terms, in the sequence, whose the decimal expansion terminates after a finite number of digits.


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