#!/usr/bin/env python
"""
 Find perfect numbers, i.e.
 those that are equal to the sum of their factors.
 Example :  6 = 1 + 2 + 3
           28 = 1 + 2 + 4 + 7 + 14 
 See http://en.wikipedia.org/wiki/Perfect_number

 The list is (6, 28, 496, 8128, 33550336, ...)
 and turns out to be 2**(n-1)*(2**n - 1) for some prime numbers n;
 these are called 'Mersenne primes'.

 --- ouput ----
 mdhcp237:Desktop$ python perfect.py
 Looking for perfect numbers up to  10000  ...
 6 is perfect =  1 + 2 + 3
 28 is perfect =  1 + 2 + 4 + 7 + 14
 496 is perfect =  1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248
   ... n = 1000 ...
   ... n = 2000 ...
   ... n = 3000 ...
   ... n = 4000 ...
   ... n = 5000 ...
   ... n = 6000 ...
   ... n = 7000 ...
   ... n = 8000 ...
 8128 is perfect =  1 + 2 + 4 + 8 + 16 + 32 + 64 + 127 + 254 + 508
                    + 1016 + 2032 + 4064
  ... n = 9000 ...
  ... n = 10000 ...
 Checking to see if mersenne( 7 ) =  8128 is perfect ...
 8128 is perfect =  1 + 2 + 4 + 8 + 16 + 32 + 64 + 127 + 254 + 508
                    + 1016 + 2032 + 4064
 Checking to see if mersenne( 11 ) =  2096128 is perfect ...
 nope.
 Checking to see if mersenne( 13 ) =  33550336 is perfect ...
 33550336 is perfect =  1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512
                        + 1024 + 2048 + 4096 + 8191 + 16382 + 32764
                        + 65528 + 131056 + 262112 + 524224 + 1048448
                        + 2096896 + 4193792 + 8387584 + 16775168
mdhcp237:Desktop$ 
 
"""

def get_factors(n):
    """ Return a list of the factors of n, including 1 but excluding n.
    >>> factors(6)
    [1, 2, 3]
    """
    answer = []
    i = 0
    while i <= n/2:
        i = i+1
        if n % i == 0:
            answer.append(i)
    return answer

def print_progress(n):
    """ Print something to show how big n is every so often. """
    interval = 1e3   # How often to show something
    if n % interval == 0:
        print "  ... n =", n, '...'

def string_sum(list):
    """ Convert a list like [1,2,3] to a string like '1 + 2 + 3'."""
    return str(list).replace(', ', ' + ').replace('[','').replace(']','')

def check_perfect(n):
    factors = get_factors(n)
    if sum(factors) == n:
        print n, "is perfect = ", string_sum(factors)
        return True
    else:
        return False

def check_mersenne(p):
    n = 2**(p-1)*(2**p-1)
    print "Checking to see if mersenne(", p, ") = ",n, "is perfect ..."
    if not check_perfect(n):
        print 'nope.'

def brute_force_search(max_n):
    n = 1
    max_n = int(max_n)
    print "Looking for perfect numbers up to ", max_n, " ..."
    while n <= max_n:
        n = n + 1
        print_progress(n)
        check_perfect(n)

brute_force_search(1e4)
check_mersenne(7)
check_mersenne(11)
check_mersenne(13)