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

$define THRESHOLD = 1 << 47

class classification
    function __construct(public seq, public aliquot) end
end

local function classify_sequence(k)
    assert(k > 0, "K must be positive")
    local last = k
    local seq = {k}
    while true do
        last = int.divisors(last, true):sum()
        seq:insert(last)
        local n = #seq
        local aliquot = ""
        if last == 0 then
            aliquot = "Terminating"
        elseif n == 2 and last == k then
            aliquot = "Perfect"
        elseif n == 3 and last == k then
            aliquot = "Amicable"
        elseif n >= 4 and last == k then
            aliquot = $"Sociable[{n - 1}]"
        elseif last == seq[n - 1] then
            aliquot = "Aspiring"
        elseif n > 3 and (last in seq:slice(2, n - 2)) then
            local ix = seq:findindex(|e| -> e == last) ?? -1
            aliquot = $"Cyclic[{n - ix}]"
        elseif n == 16 or last > THRESHOLD then
            aliquot = "Non-terminating"
        end
        if aliquot != "" then return new classification(seq, aliquot) end
    end
end

print("Aliquot classifications - periods for Sociable/Cyclic in square brackets:\n")
for k = 1, 10 do
    local c = classify_sequence(k)
    fmt.print("%2d: %-15s %,s", k, c.aliquot, c.seq)
end

print()
local a = {11, 12, 28, 496, 220, 1184, 12496, 1264460, 790, 909, 562, 1064, 1488}
for a as k do
    local c = classify_sequence(k)
    fmt.print("%7d: %-15s %,s", k, c.aliquot, c.seq)
end

print()
local k = 15355717786080
local c = classify_sequence(k)
fmt.print("%d: %-15s %,s", k, c.aliquot, c.seq)