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%I #40 May 26 2021 15:33:02
%S 0,0,2,6,26,49,154,258,666,2404,3588,11096,22477,31620,61247,157725,
%T 387527,518155,1208470,2086019,2726745,5975695,9935799,20882243,
%U 54355088,86547260,108874661,171286370,214236058,333331046,1486031972,2246585402,4132451733
%N Number of partitions of prime(n) containing a prime number of primes.
%H David A. Corneth, <a href="/A343753/b343753.txt">Table of n, a(n) for n = 1..700</a>
%e a(4) = 6 because there are 6 partitions of prime(4) = 7 that contain a prime number of primes (including repetitions). These partitions are [5,2], [3,3,1], [3,2,2], [3,2,1,1], [2,2,2,1], [2,2,1,1,1].
%t nterms=20;Table[Total[Map[If[PrimeQ[Count[#, _?PrimeQ]],1,0] &,IntegerPartitions[Prime[n]]]],{n,1,nterms}]
%o (PARI) forprime(p=2, 67, my(m=0); forpart(X=p, my(j=0); for(k=1, #X, if(isprime(X[k]), j++));if(isprime(j),m++)); print1(m, ", ")) \\ _Hugo Pfoertner_, May 01 2021
%Y Cf. A000040, A058698, A235945, A343813.
%K nonn
%O 1,3
%A _Paolo Xausa_, May 01 2021