Problem Statement

A positive integer n is an arithmetic number if the average of its positive divisors is also an integer. Clearly all odd primes p must be arithmetic numbers because their only divisors are 1 and p whose sum is even and hence their average must be an integer. However, the prime number 2 is not an arithmetic number because the average of its divisors is 1.5. 30 is an arithmetic number because its 7 divisors are: [1, 2, 3, 5, 6, 10, 15, 30], their sum is 72 and average 9 which is an integer. Calculate and show here:

1. The first 100 arithmetic numbers.
2. The xth arithmetic number where x = 1,000 and x = 10,000.
3. How many of the first x arithmetic numbers are composite. Note that, technically, the arithmetic number 1 is neither prime nor composite. Carry out the same exercise in 2. and 3. above for x = 100,000 and x = 1,000,000.

Let's start with the solution:

use Prime::Factor;
use Lingua::EN::Numbers;

my @arithmetic = lazy (1..∞).hyper.grep: { my @div = .&divisors; @div.sum %% @div }

say "The first { .Int.&cardinal } arithmetic numbers:\n", @arithmetic[^$_].batch(10)».fmt("%{.chars}d").join: "\n" given 1e2;

for 1e3, 1e4, 1e5, 1e6 {
    say "\nThe { .Int.&ordinal }: { comma @arithmetic[$_-1] }";
    say "Composite arithmetic numbers ≤ { comma @arithmetic[$_-1] }: { comma +@arithmetic[^$_].grep({!.is-prime}) - 1 }";
}