Euler Phi Function of 666 equals Product of Digits

Theorem
The number $666$ has the following interesting property:


 * $\map \phi {666} = 6 \times 6 \times 6$

where $\phi$ denotes the Euler $\phi$ function.

Proof
From Euler Phi Function of Integer:
 * $\ds \map \phi n = n \prod_{p \mathop \divides n} \paren {1 - \frac 1 p}$

where $p \divides n$ denotes the primes which divide $n$.

We have that:
 * $666 = 2 \times 3^2 \times 37$

Thus:

Also see

 * Numbers for which Euler Phi Function equals Product of Digits