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Let the partition function P(n)P(n)P(n) enumerate the ways nnn can be expressed as a distinct sum of positive integers, e.g. P(4)=5P(4) = 5P(4)=5 since 4=3+1=2+2=2+1+1=1+1+1+14 = 3+1 = 2+2 = 2+1+1 = 1+1+1+14=3+1=2+2=2+1+1=1+1+1+1 are the only ways to represent 444.
∏p prime[∑n=0∞P(n)p−n]\prod_{p \ \text{prime}} \left[ \sum_{n=0}^{\infty} P(n)p^{-n} \right]p prime∏[n=0∑∞P(n)p−n]
Does the above product converge?
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