#!/usr/bin/python2.4



def product(numbers):
	total = 1
	for number in numbers:
		total *= number
	return total

def pairOff(firstPart, secondParts):
	pairs = []
	for part in secondParts:
		if type(part) is list:
			pairs.append([firstPart] + part)
		else:
			pairs.append([firstPart, part])
	return pairs

def makeCombos(elements):
	combos = []
	rElements = list(elements)
	for element in elements:
		combos.append([element])
		rElements.remove(element)
		combos += pairOff(element, makeCombos(rElements))
	return combos


def combinations(elements):
	combos = []
	for element in elements:
		combos.append([element])
	currentSet = list(combos)
	for length in range(len(elements)):
		lastSet = currentSet
		currentSet = []
		for element in elements:
			for firstPart in lastSet:
				if (firstPart.count(element)  < length) and (firstPart.count(element)  < elements.count(element)):
					print firstPart +[element]
					currentSet.append(firstPart +[element])
		combos += currentSet
	return combos

def primeFactors(number):
	if number == 1:
		return [1]
	else:
		factor = 2
		while factor <= number:
			if (number % factor) == 0:
				return [factor] + primeFactors(number/factor)
			factor += 1
		return []

def properFactors(number):
	propFacts = factors(number)
	propFacts.remove(number)
	return propFacts

def factors(number):
	facts = []
	primeFacts = primeFactors(number)
	comboPrimeFacts = makeCombos(primeFacts)
	for combo in comboPrimeFacts:
		facts.append(product(combo))
	facts = list(set(facts))
	facts.sort()
	return facts

for number in [15, 220, 381654729, 36, 8128, 284, 386451729, 28]:
	print
	print str(number) + ":"
	attributes = []
	pFacts = properFactors(number)
	strPFacts = []
	for pFact in pFacts:
		strPFacts.append(str(pFact))
	factSum = sum(pFacts)
	print "\tdetermining factor sum:", "+".join(strPFacts), " = ", factSum
	if number > factSum:
		attributes.append("C: deficient")
	elif number < factSum:
		attributes.append("A: abundant")
	elif number == factSum:
		attributes.append("B: perfect")
	pFactsOfFactSum = properFactors(factSum)
	factSumOfFactSum = sum(pFactsOfFactSum)
	strPFactsOfFactSum = []
	for otherFact in pFactsOfFactSum:
		strPFactsOfFactSum.append(str(otherFact))
	print "\tdetermining amicability:", "+".join(strPFactsOfFactSum), " = ", factSumOfFactSum
	if (factSumOfFactSum == number) and (number != factSum):
		attributes.append("E: amicable with " + str(factSum))
	if len(str(number)) == 9:
		isDelectable = 1
		for digit in range(1,10):
			isDelectable  *= str(number).count(str(digit))
		if isDelectable == 1:
			for digit in range(1,10):
				isDelectable += (int(str(number)[:digit]) % digit)
			if isDelectable == 1:
				attributes.append("D: delectable!")
	print "\t" + "; ".join(attributes)