What is the sum of all the simplest proper fractions whose denominator is 2009?
分母是2009的所有最简真分数之和是多少．
<gadget id="calculator">1 / 7</gadget>
<output>1/7 = around 0.142857</output>

<gadget id="calculator">1 - (1/7)</gadget>
<output>6/7 = around 0.857143</output>

<gadget id="calculator">1 / 41</gadget>
<output>1/41 = around 0.02439</output>

<gadget id="calculator">1 - (1/41)</gadget>
<output>40/41 = around 0.97561</output>

<gadget id="calculator">(40/41) / 2</gadget>
<output>20/41 = around 0.487805</output>

<gadget id="calculator">2_009 * (6/7) * (20/41)</gadget>
<output>840</output>

<result>840</result>