## Challenge 334: Look for the Least

(i) What is the smallest positive integer with exactly seven factors? Or with exactly eight factors?

(ii) Find a rule for generating the sequence below and use it determine the 12^{th} and 14^{th} terms in the sequence below:

1, 2, 4, 6, 16, 12, 64, 24, …

Explain the rule you use clearly!