Let $q$ be a power of a prime, let $n \in \mathbb{N}$. Is the value of the following sum known?
$$ \sum_{d \mid q^n-1} \mu\left( \dfrac{q^n-1}{d} \right) q^{ord_d(q)}, $$ where $ord_d(q)$ denotes the multiplicative order of $q$ modulo $d$? Thanks!
2026-03-25 16:13:30.1774455210
Value of a Moebius sum
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