Question 93
Is there a positive integer sequence $a_1, a_2, \dots$ that contains every positive integer exactly once and such that
$$
\tau(na_{n+1}^n + (n+1)a_n^{n+1})
$$
is divisible by $n$ for every positive integer $n$? (Here $\tau(n)$ is the number of positive divisors of $n$.)
$$
\tau(na_{n+1}^n + (n+1)a_n^{n+1})
$$
is divisible by $n$ for every positive integer $n$? (Here $\tau(n)$ is the number of positive divisors of $n$.)