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a(n) = p(P(n)), P = primes (A000040), p = partition numbers (A000041).
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%I #26 Jul 11 2023 17:56:18

%S 2,3,7,15,56,101,297,490,1255,4565,6842,21637,44583,63261,124754,

%T 329931,831820,1121505,2679689,4697205,6185689,13848650,23338469,

%U 49995925,133230930,214481126,271248950,431149389,541946240,851376628,3913864295,5964539504,11097645016

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

%C Number of partitions of n-th prime. - _Omar E. Pol_, Aug 05 2011

%H Reinhard Zumkeller, <a href="/A058698/b058698.txt">Table of n, a(n) for n = 1..500</a>

%F a(n) = A000041(A000040(n)). - _Omar E. Pol_, Aug 05 2011

%e a(2) = 3 because the second prime is 3 and there are three partitions of 3: {1, 1, 1}, {1, 2}, {3}.

%t Table[PartitionsP[Prime[n]], {n, 30}] (* _Vladimir Joseph Stephan Orlovsky_, Dec 05 2008 *)

%o (Haskell)

%o import Data.MemoCombinators (memo2, integral)

%o a058698 n = a058698_list !! (n-1)

%o a058698_list = map (pMemo 1) a000040_list where

%o pMemo = memo2 integral integral p

%o p _ 0 = 1

%o p k m | m < k = 0

%o | otherwise = pMemo k (m - k) + pMemo (k + 1) m

%o -- _Reinhard Zumkeller_, Aug 09 2015

%Y Cf. A058697.

%Y Cf. A000040, A000041, A260798.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Dec 31 2000