Compute Euler's Totient Function (\(\phi(n)\)). Provides the
count of \(k\) integers that are coprime with \(n\) such that
\(1 \le k \le n\) and \(gcd(n,k) = 1\).

Fast functions for dealing with prime numbers, such as testing
whether a number is prime and generating a sequence prime numbers.
Additional functions include finding prime factors and Ruth-Aaron pairs,
finding next and previous prime numbers in the series, finding or estimating
the nth prime, estimating the number of primes less than or equal to an
arbitrary number, computing primorials, prime k-tuples (e.g., twin primes),
finding the greatest common divisor and smallest (least) common multiple,
testing whether two numbers are coprime, and computing Euler's totient
function. Most functions are vectorized for speed and convenience.

Oliver Keyes

primes

Fast Functions for Prime Numbers

Os Keyes

Paul Egeler

phi function

<dl><dt>n</dt>
<dd>an integer vector.</dd></dl>

Arguments

Author

Euler's Totient Function — phi

<dl>

<dt>n</dt>
<dd>an integer vector.</dd>

</dl>

phi: Euler's Totient Function

Description

Usage

Value

Arguments

Author

References

See Also

Examples