Totient Function - Maple Help
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NumberTheory

  

Totient

  

Euler's totient function

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Totient(n)

 

phi(n)

varphi(n)

Parameters

n

-

positive integer

Description

• 

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 , and varphi(8) is equivalent to .

Examples

(1)

If two integers n and m are coprime, then Totient(n)*Totient(m) = Totient(m*n). That is, the totient function is multiplicative.

(2)

(3)

The totient of any prime p is equal to p-1.

(4)

(5)

The following command plots the values of Totient(n) for n from  to .

Compatibility

• 

The NumberTheory[Totient] command was introduced in Maple 2016.

• 

For more information on Maple 2016 changes, see Updates in Maple 2016.

See Also

NumberTheory

NumberTheory[InverseTotient]

 


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