Question 114
say that a positive integer $b$ is *fortunate* if for every positive integer $a$, a number $b$ divides $a^2$ whenever $b^2$ divides $a^5$. Find the number of fortunate positive integers which are less than $2010$. (P. Kozhevnikov) Natural number $b$ is called successful if for any natural $a$ such that $a^5$ is divided into $b^2$, the number $a^2$ is divided by $b$. Find the number of successful natural numbers smaller than $2010$. (P. Kozhevnikov)