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

1,3

Links

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

Example

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].

Mathematica

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

Prog

(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

Crossrefs

Cf. A000040, A058698, A235945, A343813.

Sequence in context: A337573 A331963 A308988 * A316469 A322116 A223094

Adjacent sequences: A343750 A343751 A343752 * A343754 A343755 A343756

Keyword

nonn

Author

Paolo Xausa, May 01 2021

Status

approved