Consecutive Integers with Same Euler Phi Value/Examples/15

Example of Consecutive Integers with Same Euler Phi Value
Let $\phi: \Z_{>0} \to \Z_{>0}$ denote the Euler $\phi$ function: the number of strictly positive integers less than or equal to $n$ which are prime to $n$.

Then:
 * $\phi \left({15}\right) = \phi \left({16}\right) = 8$

Proof
From Euler Phi Function of 15:
 * $\phi \left({15}\right) = 8$

From the corollary to Euler Phi Function of Prime Power:
 * $\phi \left({16}\right) = \phi \left({2^4}\right) = 2^{4 - 1} = 8$

Hence the result.