A343753 Number of partitions of prime(n) containing a prime number of primes.

0, 0, 2, 6, 26, 49, 154, 258, 666, 2404, 3588, 11096, 22477, 31620, 61247, 157725, 387527, 518155, 1208470, 2086019, 2726745, 5975695, 9935799, 20882243, 54355088, 86547260, 108874661, 171286370, 214236058, 333331046, 1486031972, 2246585402, 4132451733

Offset: 1

Author

Paolo Xausa, May 01 2021

Keywords

• nonn

Examples

			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].
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..700

Crossrefs

Cf. A000040, A058698, A235945, A343813.

Programs

Mathematica

nterms=20;Table[Total[Map[If[PrimeQ[Count[#, _?PrimeQ]],1,0] &,IntegerPartitions[Prime[n]]]],{n,1,nterms}]

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