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

local function is_square_free(n)
    local i = 2
    local sq = i * i
    while sq <= n do
        if n % sq == 0 then return false end
        i = (i > 2) ? i + 2 : i + 1
        sq = i * i
    end
    return true
end

local function mu(n)
    assert(n >= 1, "Argument must be a positive integer")
    if n == 1 then return 1 end
    local sq_free = is_square_free(n)
    local factors = int.factors(n)
    if sq_free and #factors % 2 == 0 then return 1 end
    if sq_free then return -1 end
    return 0
end

print("The first 199 Möbius numbers are:")
for i = 0, 9 do
    for j = 0, 19 do
        if i == 0 and j == 0 then
            io.write("    ")
        else
            fmt.write("% 3d ", mu(i * 20 + j))
        end
    end
    print()
end