# Generation partition

Calculus Level 3

Let the partition function $$P(n)$$ enumerate the ways $$n$$ can be expressed as a distinct sum of positive integers, eg $$P(4) = 5$$ since $$4 = 3+1 = 2+2 = 2+1+1 = 1+1+1+1$$ are the only ways to represent $$4$$.

$\prod_{p \ \text{prime}} \left[ \sum_{n=0}^{\infty} P(n)p^{-n}(1-\frac{1}{p}) \right]$

Does the above product converge?

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