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Let 
$g\geqslant 2$. A real number is said to be 
$g$-normal if its base 
$g$ expansion contains every finite sequence of digits with the expected limiting frequency. Let 
$\unicode[STIX]{x1D711}$ denote Euler’s totient function, let 
$\unicode[STIX]{x1D70E}$ be the sum-of-divisors function, and let 
$\unicode[STIX]{x1D706}$ be Carmichael’s lambda-function. We show that if 
$f$ is any function formed by composing 
$\unicode[STIX]{x1D711}$, 
$\unicode[STIX]{x1D70E}$, or 
$\unicode[STIX]{x1D706}$, then the number obtained by concatenating the base 
$$\begin{eqnarray}0.f(1)f(2)f(3)\cdots\end{eqnarray}$$
$g$ digits of successive 
$f$-values is 
$g$-normal. We also prove the same result if the inputs 
$1,2,3,\ldots$ are replaced with the primes 
$2,3,5,\ldots$. The proof is an adaptation of a method introduced by Copeland and Erdős in 1946 to prove the 10-normality of 
$0.235711131719\cdots \,$.
