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A Divisor-Weighted Golomb Sequence: Zeta Asymptotics and Arithmetic Fluctuations
We study a divisor-weighted version of Golomb's self-description: the nondecreasing sequence $A$ in which each positive integer $m$ occurs $\sum_{d\mid m}A(d)$ times. This rule has a unique solution, and $$ A(n)\sim Cn^{φ-1},\quad C=\left(\fracφ{ζ(φ)}\right)^{2-φ},\quad φ=\frac{1+\sqrt{5}}{2}. $$ Th
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