Let $P(x)$ be an irreducible quadratic polynomial in $\mathbb{Z}[x]$. We show that for almost all $n$, $P(n)$ does not lie in the range of Euler's totient function.
Euler's Function on Products of Primes in Progressions
On common values of $φ(n)$ and $σ(m)$, II
Sparse subsets of the natural numbers and Euler's totient function
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