Dividing sequences

Algebra Level pending

Tom takes two sequences \(\{1 , 9 , 36 , 100 , 225 , 441\}\) and \(\{1 , 5 , 14 , 30 , 55 , 91\}\). Tom divides the \(n^\text{th}\) term of the first sequence by the \(n^\text{th}\) term of the second sequence. For how many values of \(n\) is the result an integer?

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