KöMaL 2005 B3859

Find all natural numbers $n$ greater than 1, for which there is an order $a_1$,$a_2$,...,$a_n$ of the numbers 1,2,3,...,$n$, such that the products $a_1$, $a_1 a_2$, $a_1 a_2 a_3$, ..., $a_1 a_2 ^{...} a_n$ divided by $n$all leave different remainders.