File:Mertensplot,n=0to2000.png

#!/usr/bin/python
import numpy as np
import matplotlib.pyplot as plt
from mpmath import *
from pylab import rcParams
rcParams['figure.figsize'] = 10, 10

def numberOfFactors(n):
        counter = 0
        while (n > 1):
                i=2
                while (i <= n):
                        if(n%i ==0):
                                n /= i
                                counter += 1
                                break
                        i += 1
        return counter

def isDivisibleBySquare(n):
        i=2
        while(i**2 <= n):
                if (n%(i**2)==0):
                        return 1
                i += 1
        return 0

def isValid(n):
        if (n <= 0):
                return 0
        elif (n-int(n) != 0):
                return 0
        return 1

def mobius(n):
        if not isValid(n):
                return 0
        elif (n==1):
                return 1
        elif(isDivisibleBySquare(n)):
                return 0
        else:
                return (-1)**numberOfFactors(n)

def mertens(n):
        return nsum(lambda x: mobius(x), [1,n])

fig, ax = plt.subplots()

x=np.arange(0,2000,1)
f=np.vectorize(mertens)
y=f(x)
plt.xlabel(r'$n$')
plt.ylabel(r'$M(n)$')

#xlabels=[item.get_text() for item in ax.get_xticklabels()]
#xlabels=[r'$0$',r'$20$',r'$40$',r'$60$',r'$80$',r'$100$']
#ax.set_xticks([0,20,40,60,80,100])
#ax.set_xticklabels(xlabels,horizontalalignment='center')

#ylabels=[item.get_text() for item in ax.get_yticklabels()]
#ylabels=[r'$-1$',r'$0$',r'$1$']
#ax.set_yticks([-1,0,1])
#ax.set_yticklabels(ylabels,verticalalignment='center')

plt.xlim(0,2000)

plt.scatter(x,y,color='Black')

plt.savefig('mertensplot,n=0to2000.png',bbox_inches='tight',pad_inches=0.15)