Consecutive Integers with Same Euler Phi Value/Examples

Examples 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 $n$.

The following are solutions to the equation:

$\phi \left({n}\right) = \phi \left({n + 1}\right)$

$\phi$ of $1$ equals $\phi$ of $2$

$\map \phi 1 = \map \phi 2 = 1$

$\phi$ of $3$ equals $\phi$ of $4$

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

$\phi$ of $15$ equals $\phi$ of $16$

$\map \phi {15} = \map \phi {16} = 8$

$\phi$ of $104$ equals $\phi$ of $105$

$\map \phi {104} = \map \phi {105} = 48$

$\phi$ of $164$ equals $\phi$ of $165$

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

$\phi$ of $194$ equals $\phi$ of $195$

$\map \phi {194} = \map \phi {195} = 96$

$\phi$ of $255$ equals $\phi$ of $256$

$\map \phi {255} = \map \phi {256} = 128$