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EulerPhi

Euler's totient function (SymPy, WMA)
This function counts positive integers up to n that are relatively prime to n.
It is typically used in cryptography and in many applications in elementary number theory.

EulerPhi[n]

returns the Euler totient function .

Compute the Euler totient function:

• • EulerPhi[9]

EulerPhi of a negative integer is same as its positive counterpart:

• • EulerPhi[-11] == EulerPhi[11]

• • EulerPhi[0]

Large arguments are computed quickly:

• • EulerPhi[40!]

EulerPhi threads over lists:

• • EulerPhi[Range[1, 17, 2]]

Above, we get consecutive even numbers when the input is prime.

Compare the results above with:

• • EulerPhi[Range[1, 17]]

  • $$\left\{1,1,2,2,4,2,6,4,6,4,10,4,12,6,8,8,16\right\}$$