Kassel and Reutenauer \cite{kassel2016fourier} introduced a $q$-analogue of the number of representations of an integer as a sum of two squares. We establish some connections between the prime factorization of $n$ and the coefficients of this $q$-analogue.
The Zassenhaus filtration, Massey Products, and Representations of Profinite Groups
Representations of integers as sums of primes from a Beatty sequence
Representations by octonary quadratic forms with coefficients $1$, $2$, $3$ or $6$
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