Euler's Totient Function - Generating Functions

Generating Functions

The Dirichlet series for φ(n) may be written in terms of the Riemann zeta function as:

The Lambert series generating function is

which converges for |q| < 1.

Both of these are proved by elementary series manipulations and the formulae for φ(n).

Read more about this topic:  Euler's Totient Function

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