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This problem trains for: AMC-8, Math Kangaroo 7-8, AMC-10.

What is the product of the prime divisors of the numbers of the form:

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where n is a positive integer?

Work on the expression to find a factoring:

equation

equation

The numbers of this form have a prime factorization of the form:

equation

The product of the prime factors is:

equation

Note that, if n is allowed to be zero, then the only prime factors remaining are 2 and 7 and the product is only 14.