# Lucky Number

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.