Revision as of 01:39, 28 November 2016

Euler's totient function $\phi$ (not to be confused with the Euler phi) is defined for $n=1,2,3,\ldots$ so that $\phi(n)$ equals the number of positive integers less than or equal to $n$ that are relatively prime to $n$.

Properties

Sum of totient equals zeta(z-1)/zeta(z) for Re(z) greater than 2
Sum of totient equals z/((1-z) squared)
Product representation of totient
Euler totient is multiplicative

Videos

Euler's Totient Function: what it is and how it works
Euler's Totient Theorem: What is Euler's Totient Theorem and Why is it useful?
Euler's Totient Function | How To Find Totient Of A Number Using Euler's Product Formula
Euler's Totient Function
Euler's totient function
Prime Factorisation and Euler Totient Function Part 14
Application of Euler Totient Function Part 16
Möbius and Euler totient functions
Euler Totient Theorem, Fermat Little Theorems
Euler's Phi Function
03 Modern cryptography 08 Euler's totient function
Euler Totient (phi) Function Examples (Part 1) (27 November 2016)

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $24.3.2 \mathrm{I}.A.$

Chebyshev $\vartheta$

Chebyshev $\psi$

Euler $\phi$

Greatest prime factor

Mangoldt

Mertens

Möbius

Liouville $\lambda$

Prime counting

Riemann-Siegel $Z$

Riemann zeta

Sum of divisors

Totient