Multicover formula for the curve-counting invariants $N_{n,\beta}$

Let $N_{n,\beta}$ be the curve-counting invariants introduced through the PT product expansion, let $n\in\mathbb Z_{>0}$, and let $\beta$ be an effective curve class. Write $k\mid(n,\beta)$ for positive integers $k$ dividing both $n$ and the class $\beta$. Multicover formula conjecture.

$$N_{n,\beta}=\sum_{k\geq 1,\,k\mid(n,\beta)}\frac{1}{k^2}N_{1,\beta/k}.$$

This formula is obtained by comparing coefficients after taking logarithms of the conjectural PT product expansion; its validity therefore remains tied to that conjectural framework.