Equal Numbers of Factors

2013, 2014 and 2015 have an interesting property regarding their factors. They all have the same number of factors: 8. What is the smallest positive integer \(N\) that has the same number of factors as \(N+1\) and \(N+2\)?

Bonus: Can you write a program that finds all of the numbers less than \(10^6\) that also have this property?

Source: 2013 Florida Fall Interschool
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