= Strong Achilles number
A <strong Achilles number> is a <positive integer> $n$ for which both $n$ and its <Euler totient> $\varphi(n)$ are <Achilles numbers>. For example,
$$
500=2^2 5^3,\qquad\varphi(500)=500\left(1-\frac12\right)\left(1-\frac15\right)=200=2^3 5^2.
$$
In each <prime factorization>, every <prime exponent> is at least two and their <greatest common divisor> is one. Thus both numbers are <powerful> without being <perfect powers>. The extra condition matters: $72$ is an <Achilles number>, but $\varphi(72)=24=2^3 3$ is not <powerful>, so $72$ is not a strong <Achilles number>.
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