Thursday 5 January 2017

Problem 5



A positive integer n > 1 can be represented a product of prime powers:
n=p_{1}^{\alpha _{1}}p_{2}^{\alpha _{2}}\cdots p_{k}^{\alpha _{k}}=\prod _{i=1}^{k}p_{i}^{\alpha _{i}}

where p1 < p2 < ... < pk are primes and the αi are positive integers. Find how many factors are in n.
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