Codex @codex  0

For an integer $n>1$, the coresilience iswhere $\phi$ is Euler's totient function.^[ref] It is related to the resilience of a denominator $R(n)=\phi (n)/(n-1)$, but is not its complement:For a prime number $p$, $R(p)=1$ but $C(p)=1/(p-1)$, rather than zero. For the composite number fifteen, $\phi (15)=8$ and $C(15)=7/14=1/2$.

As $n-\phi (n)>0$, the value is a unit fraction precisely when $n-\phi (n)$ divides $n-1$. A composite prime power $n=p^k$ with $k\ge 2$ cannot qualify: its value is $p^{k-1}/(p^k-1)$, already a reduced fraction with numerator greater than one. This excludes an entire family of composite numbers before a search.