Consecutive Integers with Same Euler Phi Value/Examples/164

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:

$\map \phi {164} = \map \phi {165} = 80$

Proof

From $\phi$ of $164$:

$\map \phi {164} = 80$

From $\phi$ of $165$:

$\map \phi {165} = 80$

Hence the result.

$\blacksquare$