# Lucky Number

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A positive integer is called "lucky number" if it has exactly $$2014$$ positive divisors and can divided by $$2014$$. Let $$k$$ denote the number of all possibilities of "lucky number" and $$a_{1},a_{2},...,a_{k}$$ are all possibilities of "lucky number". If there is a positive integer $$p$$ which satisfies $2014^p|a_{1}a_{2}a_{3}...a_{k}$ ,then determine the maximum value of $$p$$ which possible.

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