do  -- Jordan-Pólya numbers - translation of XPL0 via Oberon-07

    local  maxFactorial = 11
    local  f = {}
    f[ 1 ] = 1 for i = 2, maxFactorial do f[ i ] = f[ i - 1 ] * i end

    local function isJordanPolya( m )
        local result, limite = false, maxFactorial + 1
        while not result and limite > 1 do
            limite = limite - 1
            local n, i = m, limite
            local fac  = f[ limite ]
            repeat
                if n % fac == 0 then
                    n      = math.floor( n / fac )
                    result = n == 1
                else
                    fac    = math.floor( fac / i )
                    i      = i - 1
                end
            until i == 1 or result
        end
        return result
    end

    local function next( n0 )
        local n = n0
        repeat
            n = n + 2
        until isJordanPolya( n )
        return n
    end

    do
        io.write( "1" )
        local n = 0
        for c = 2, 50 do
            n = next( n )
            io.write( " " .. n )
        end
        n = 100000000
        while n > 1 and not isJordanPolya( n ) do
            n = n - 2
        end
        io.write( "\nThe largest Jordan-Pólya number before 100 million: " .. n .. "\n" )
    end
end