Consecutive Integers with Same Euler Phi Value/Examples/3

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:

$\map \phi 3 = \map \phi 4 = 2$

Proof

From Euler Phi Function of 3:

$\map \phi 3 = 2$

From the corollary to Euler Phi Function of Prime Power:

$\map \phi 4 = \map \phi {2^2} = 2^{2 - 1} = 2$

Hence the result.

$\blacksquare$