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A058698 a(n) = p(P(n)), P = primes (A000040), p = partition numbers (A000041).

%I A058698 #26 Jul 11 2023 17:56:18
%S A058698 2,3,7,15,56,101,297,490,1255,4565,6842,21637,44583,63261,124754,
%T A058698 329931,831820,1121505,2679689,4697205,6185689,13848650,23338469,
%U A058698 49995925,133230930,214481126,271248950,431149389,541946240,851376628,3913864295,5964539504,11097645016
%N A058698 a(n) = p(P(n)), P = primes (A000040), p = partition numbers (A000041).
%C A058698 Number of partitions of n-th prime. - _Omar E. Pol_, Aug 05 2011
%H A058698 Reinhard Zumkeller, <a href="/A058698/b058698.txt">Table of n, a(n) for n = 1..500</a>
%F A058698 a(n) = A000041(A000040(n)). - _Omar E. Pol_, Aug 05 2011
%e A058698 a(2) = 3 because the second prime is 3 and there are three partitions of 3: {1, 1, 1}, {1, 2}, {3}.
%t A058698 Table[PartitionsP[Prime[n]], {n, 30}] (* _Vladimir Joseph Stephan Orlovsky_, Dec 05 2008 *)
%o A058698 (Haskell)
%o A058698 import Data.MemoCombinators (memo2, integral)
%o A058698 a058698 n = a058698_list !! (n-1)
%o A058698 a058698_list = map (pMemo 1) a000040_list where
%o A058698    pMemo = memo2 integral integral p
%o A058698    p _ 0 = 1
%o A058698    p k m | m < k     = 0
%o A058698          | otherwise = pMemo k (m - k) + pMemo (k + 1) m
%o A058698 -- _Reinhard Zumkeller_, Aug 09 2015
%Y A058698 Cf. A058697.
%Y A058698 Cf. A000040, A000041, A260798.
%K A058698 nonn
%O A058698 1,1
%A A058698 _N. J. A. Sloane_, Dec 31 2000