Möbius function visualization using mathplotlib

mobius.py

#!/usr/bin/env python
# -*- coding: utf-8 -*-

__author__ = 'Vital Kolas'
__version__ = '0.0.1'

from pylab import *
from collections import Counter

if __name__ == '__main__':

    max_value = 30

    primaries = Counter()
    numbers = range(1, max_value)
    mob = []
    for value in numbers:
        # check if square-free
        if value == 1:
            mob.append(1)
        else:
            is_square_free = True
            for primary in primaries:
                perfect_square = primary ** 2
                if value >= perfect_square and value % perfect_square == 0:
                    is_square_free = False
                    break
            # count prime factors
            factor_count = 1
            for primary in primaries:
                if value % primary == 0:
                    factor_count = primaries[primary] + primaries[value // primary]
                    break
            # calc Möbius function
            if is_square_free:
                mob_value = -1 if factor_count % 2 else 1
            else:
                mob_value = 0

            primaries[value] = factor_count
            mob.append(mob_value)

    plot(numbers, mob, marker = 'o', linestyle = '')

    ylim([-2, 2])
    grid(True)
    show()