Browsing through OESIS I have found that if $p_p(n)$ denotes the number of partitions of $n$ into prime parts then $p_p(n) = O(e^{\frac{2 \Pi}{\sqrt{3}}\sqrt{n/\log n}})$.

I am interested in the asymptotic behaviour of a more specific function - $p(n,k)$ defined as the number of partitions of $n$ into $k$ parts such that every part is an odd prime. (for example one such partition of 13 would be 7+3+3)

Is there any known literature for looking up such identities? Or perhaps, is there an easy way to derive an asymptotic bound for $p(n,k)$ ?

  • $\begingroup$ asymptotics is respectively standard to obtain, but would you please specify the relation between $n$ and $k$? $\endgroup$ – Fedor Petrov Mar 14 '11 at 11:26
  • $\begingroup$ Ideally I would like k to run from 1 to n/3 $\endgroup$ – Jernej Mar 14 '11 at 11:32

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