Question 25
In his last research, professor $P$ was concentrating on natural numbers with a certain property. It is known that whenever a natural number $x$ has this property, all multiples of $x$ also have this property. Let $a_1, \dots, a_n$ be positive integers such that all their divisors that are greater than one have the property professor $P$ studied. Is it true that all divisors greater than one of the product $a_1 \dots a_n$ definitely have this property?