%I #14 Mar 19 2024 08:32:28

%S 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,

%T 9,9,11,11,11,13,12,14,15,14,17,15,17,19,18,21,21,21,24,24,26,28,27,

%U 30,30,32,35,34,37,37,39,41,43,45,46,48,51,53,56,58,59,61,64,66,70,71,73

%N Number of partitions of n into distinct Chen primes.

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

%H Charles R Greathouse IV, <a href= "/A112022/b112022.txt" >Table of n, a(n) for n = 0..10000</a>

%F G.f.: Product_{k>=1} (1 + x^A109611(k)). - _Andrew Howroyd_, Dec 28 2017

%t terms = 81;

%t gf = Times @@ (1 + x^SequencePosition[ PrimeOmega[ Range[terms]], {1, _, 1|2}][[All, 1]]) + O[x]^terms;

%t CoefficientList[gf, x] (* _Jean-François Alcover_, Jul 02 2018 *)

%o (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

%Y Cf. A112021, A112020, A109611.

%K nonn

%O 0,6

%A _Reinhard Zumkeller_, Aug 26 2005