File:Mangoldtglyph.png

#!/usr/bin/python
import numpy as np
import matplotlib.pyplot as plt
import fractions
from mpmath import *
from pylab import rcParams
rcParams['figure.figsize'] = 2.4,2.4

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

def isPrimePower (n , d ):
        return ( math . log (n , d ) - int ( math . log (n , d ))==0)



def Mangoldt ( n ):
        if not isValid ( n ):
                return 0
        d = 2
        while (d <= n ):
                # Find a divisor
                if ( n % d ==0):
                        # Check if n is d to some power
                        if ( isPrimePower (n , d )):
                                return log ( d )
                        else :
                                # If not , it must be a product
                                # of different divisors .
                                return 0
                d += 1
        return 0

x=np.arange(0,400,1)
f=np.vectorize(mangoldt)
y=f(x)

x2=np.arange(-500,1000,0.1)
def g(x):
        return 0
h=np.vectorize(g)
y2=h(x2)

fig, ax = plt.subplots()
ax.spines['top'].set_color('none')
ax.spines['left'].set_color('none')
ax.spines['right'].set_color('none')
plt.tick_params(axis='x', which='both', bottom='off', top='off', labelbottom='off')
plt.tick_params(axis='y', which='both', left='off', right='off', labelleft='off')

plt.scatter(x,y,linewidth=1,color='Black')
plt.plot(x2,y2,linewidth=1,color='Black')
plt.plot(y2,x2,linewidth=1,color='Black')

plt.xlim(0,400)
plt.ylim(-0.3,6)

plt.savefig('mangoldtglyph.png',bbox_inches='tight',pad_inches=0.0)