# 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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