Let n be a positive integer and suppose we factor n into primes as follows: n D p e1 1 p

Chapter 39, Problem 39.14

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Let n be a positive integer and suppose we factor n into primes as follows: n D p e1 1 p e2 2 p et t where the pj s are distinct primes and the ej s are natural numbers. Find a formula for the number of positive divisors of n. For example, if n D 18, then n has six positive divisors: 1, 2, 3, 6, 9, and 18.

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