File:EulerPhi.svg
Summary
| Description |
English: Plot of the first 1000 values of the en:Euler's totient function. Svg version of Image:EulerPhi.PNG
|
| Date | |
| Source | Own workCategory:Unspec SVG created with Matplotlib#00050718EulerPhi.svg |
| Author | Pietro Battiston (it:User:Toobaz) |
| Other versions | Image:EulerPhi.PNG |
Created with the following script, ran in "ipython -pylab":
xlabel('n')
ylabel('$\phi(n)$')
plot([None]+[fi(i) for i in range(1,1000)], 'b.')
"fi" is the Euler φ, defined for instance as:
def fattorizza(n):
c = 0
f = {}
for i in xrange( 2, int(sqrt(n))+1 ):
if not n%i:
f[i] = 1
n /= i
while not n%i:
f[i] += 1
vn = n
n /= i
if n == 1:
return f
f[n] = 1
return f
def fi(n):
if n == 1:
return 1
fi = 1
f = fattorizza(n)
for p in f:
k = f[p]
fi *= (p-1)*p**(k-1)
return fi
Licensing
I, the copyright holder of this work, hereby publish it under the following licenses:
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. |
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