this is an efficient aliqout sequence program. you begin by finding the proper factors of a number you put in.then you find the proper factor of the sum of the proper factors.there are two ways an aliqout sequence can end:a prime number,where it then goes to one and then to zero, or a perfect number, where it repeats, like 6,6,6,6, and so on. this program detects both of those.there are two other ways that this program does not detect but will be added in an update soon:amicable pairs and sociable groups of numbers.amicable pairs are two numbers in which the proper factors of one is equal to the other, and vice versa. sociable groups of numbers are like amicable pairs, but they are in bigger groups. in 1888, eugene catalan conjectured that every aliquot sequence must end in one of these ways. Some numbers are making mathematiciansdoubt this conjecture:276 is one of many numbers which currently has no end. Don't beleive me? try it in turbo mode, and put in 276. you will be staring at a blank screen forever. Well, ther will be numbers moving. have fun!
