test.py

#!/usr/bin/env python

import doctest
import itertools as it
import math


def divisor_generator(num):
    """

    >>> list(divisor_generator(100))
    [1, 2, 4, 5, 10, 20, 25, 50]

    """
    large_divisors = []
    yield 1
    for i in range(2, int(math.sqrt(num) + 1)):
        if num % i is 0:
            yield i
            if i is not num / i:
                large_divisors.insert(0, num / i)
    for divisor in large_divisors:
        yield divisor


def powerset(xs):
    """

    >>> list(powerset([1, 2, 3]))
    [(), (1,), (2,), (3,), (1, 2), (1, 3), (2, 3), (1, 2, 3)]

    """
    return it.chain.from_iterable(
        it.combinations(xs, n) for n in range(len(xs) + 1))


def check_pitch(num):
    """

    >>> check_pitch(35)
    False
    >>> check_pitch(70)
    True

    """
    divisors = list(divisor_generator(num))
    if sum(divisors) <= num:
        return False

    subsums = set(map(sum, powerset(divisors)))
    if not num in subsums:
        return True


def pitch(mx):
    """

    >>> pitch(553)
    70

    """
    for num in range(1, mx + 1):
        if check_pitch(num):
            return num


if __name__ == "__main__":
    doctest.testmod()