Euler totient

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 $n$.

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  Graph of $\phi$ to $3500$.

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

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References

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