Input: Any fraction between 0 and 1, Output: A set of distinct natural numbers, the sum of reciprocals of these numbers is the input

breakIntoFractions.py

from fractions import gcd

def addToList(denominators, q):
	if(q in denominators):
		addToList(denominators, q+1)
		addToList(denominators, q*(q+1))
	else:
		denominators.append(q)

def breakIntoFractions(denominators, p, q):
	if(p == 1):
		addToList(denominators, q)
	else:
		addToList(denominators, q)
		breakIntoFractions(denominators, p-1, q)

def main(p, q):
	if(p < q and p != 0):
		denominators = []
		div = gcd(p, q)
		breakIntoFractions(denominators, p/div, q/div)
		print "(" + str(p) + "/" + str(q) + "): " + str(denominators)
	else:
		print "The fraction should be between 0 and 1."
		
p = int(raw_input("Enter numerator:   "))
q = int(raw_input("Enter denominator: "))
main(p, q)