Euler's totient function
The Totient function computes Euler's totient function.
Given a positive integer n, Totient(n) returns the number of positive integers coprime to n and not greater than n.
phi and varphi are aliases of Totient.
You can enter the commands phi and varphi using either the 1-D or 2-D calling sequence. For example, phi(8) is equivalent to φ⁡8, and varphi(8) is equivalent to ϕ⁡8.
If two integers n and m are coprime, then Totient(n)*Totient(m) = Totient(m*n). That is, the totient function is multiplicative.
The totient of any prime p is equal to p-1.
The following command plots the values of Totient(n) for n from 2 to 1000.
The NumberTheory[Totient] command was introduced in Maple 2016.
For more information on Maple 2016 changes, see Updates in Maple 2016.
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