A112022 Number of partitions of n into distinct Chen primes.

1, 0, 1, 1, 0, 2, 0, 2, 1, 1, 2, 1, 2, 2, 2, 2, 3, 2, 4, 3, 4, 4, 4, 5, 5, 5, 6, 5, 6, 7, 6, 9, 7, 9, 9, 9, 11, 11, 11, 13, 12, 14, 15, 14, 17, 15, 17, 19, 18, 21, 21, 21, 24, 24, 26, 28, 27, 30, 30, 32, 35, 34, 37, 37, 39, 41, 43, 45, 46, 48, 51, 53, 56, 58, 59, 61, 64, 66, 70, 71, 73

Offset: 0

Author

Reinhard Zumkeller, Aug 26 2005

Keywords

• nonn

Comments

a(n) = A000586(n) for n <= 42.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A112021, A112020, A109611.

Programs

Mathematica

terms = 81;
gf = Times @@ (1 + x^SequencePosition[ PrimeOmega[ Range[terms]], {1, _, 1|2}][[All, 1]]) + O[x]^terms;
CoefficientList[gf, x] (* Jean-François Alcover, Jul 02 2018 *)

PARI

P=1+O(x^1001); forprime(p=2,1e3,if(bigomega(p+2)<3,P*=1+x^p)); Vec(P) \\ Charles R Greathouse IV, May 13 2013

Formula

G.f.: Product_{k>=1} (1 + x^A109611(k)). - Andrew Howroyd, Dec 28 2017