local int = require "int"
local fmt = require "fmt"
require "table2"

local arithmetic = {1}
local primes = {}
local limit = 1e6
local n = 3
while #arithmetic < limit do
    local divs = int.divisors(n)
    if #divs == 2 then
        primes:insert(n)
        arithmetic:insert(n)
    else
        local mean = divs:mean()
        if mean % 1 == 0 then arithmetic:insert(n) end
    end
    n += 1
end
print("The first 100 arithmetic numbers are:")
fmt.tprint("%3d", arithmetic:slice(1, 100), 10)

for {1e3, 1e4, 1e5, 1e6} as x do
    local last = arithmetic[x]
    fmt.print("\nThe %,sth arithmetic number is: %,s", x, last)
    local pcount = primes:findindex(|p| -> p >= last, 1, true)
    if !pcount then
        pcount = #primes
    elseif !int.isprime(last) then
        pcount -= 1;
    end
    local comp = x - pcount - 1  -- 1 is not composite
    fmt.print("The count of such numbers <= %,s which are composite is %,s.", last, comp)
end