Question 16
We say that a natural number $n \ge 3$ is almost square-free if there exists a prime number $p$, with $p \equiv 1 \pmod 3$, such that $n$ is divisible by $p^2$, and the number $\frac{n}{p}$ is square-free (i.e., not divisible by the square of any prime number).
Show that, for any natural number $n$ that is almost square-free, the ratio between twice the sum of the divisors of $n$ and the number of divisors of $n$ is a natural number.
Lucian Petrescu
Show that, for any natural number $n$ that is almost square-free, the ratio between twice the sum of the divisors of $n$ and the number of divisors of $n$ is a natural number.
Lucian Petrescu