Question 76
A positive integer $N$ is said to be an "*n*-good number" if it satisfies the following two properties:
(Property 1) $N$ is divisible by at least $n$ distinct primes
(Property 2) There exist distinct positive divisors $1, x_2, \dots, x_n$ of $N$ such that
$$
1 + x_2 + \dots + x_n = N.
$$
Show that there exists an "*n*-good number" for each $n \ge 6$.
(Property 1) $N$ is divisible by at least $n$ distinct primes
(Property 2) There exist distinct positive divisors $1, x_2, \dots, x_n$ of $N$ such that
$$
1 + x_2 + \dots + x_n = N.
$$
Show that there exists an "*n*-good number" for each $n \ge 6$.