Euler Phi Function of 2 times Odd Prime

Theorem

Let $n \in \Z_{>0}$ be a semiprime of the form $2 p$, where $p$ is an odd prime.

Let $\map \phi n$ denote the Euler $\phi$ function.

Then:

$\map \phi n = p - 1$

Proof

By definition $n$ is a semiprime.

As $p$ is an odd prime, $n$ is not square.

Thus from Euler Phi Function of Non-Square Semiprime:

$\map \phi n = \paren {2 - 1} \paren {p - 1}$

Hence the result.

$\blacksquare$

Examples

$\phi$ of $14$

$\map \phi {14} = 6$

$\phi$ of $146$

$\map \phi {146} = 72$

$\phi$ of $362$

$\map \phi {362} = 180$