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2013 PUMaC Number Theory A3/B5

Source:

November 24, 2013
number theoryprime factorization

Problem Statement

Let AA be the greatest possible value of a product of positive integers that sums to 20142014. Compute the sum of all bases and exponents in the prime factorization of AA. For example, if A=7ā‹…115A=7\cdot 11^5, the answer would be 7+11+5=237+11+5=23.
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