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between 2000 and 2010, probability that a random divisor is <=45 largest?

Source: Austrian Regional Competition For Advanced Students 2013, p1

February 19, 2020
Divisorsprobabilitynumber theory

Problem Statement

For which integers between 20002000 and 20102010 (including) is the probability that a random divisor is smaller or equal 4545 the largest?