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Generating function of partitions of $n$ in $k$ prime parts.
I have been looking for the function that generates the partitions of $n$ into $k$ parts of prime numbers (let's call it $Pi_k(n)$). For example: $Pi_3(9)=2$, since $9=5+2+2$ and $9=3+3+3$.
I know ...
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Express number of partitions into prime numbers using partitions into natural numbers.
Let $P(n)$ is number of partitions of $n$ into natural numbers.
$R(n)$ is number of partitions of $n$ into prime numbers.
Is there any expression that relates $P(n)$ , and $R(n)$? I look for ...
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