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A112022 Number of partitions of n into distinct Chen primes.

%I A112022 #14 Mar 19 2024 08:32:28
%S A112022 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 A112022 9,9,11,11,11,13,12,14,15,14,17,15,17,19,18,21,21,21,24,24,26,28,27,
%U A112022 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 A112022 Number of partitions of n into distinct Chen primes.
%C A112022 a(n) = A000586(n) for n <= 42.
%H A112022 Charles R Greathouse IV, <a href="/A112022/b112022.txt">Table of n, a(n) for n = 0..10000</a>
%F A112022 G.f.: Product_{k>=1} (1 + x^A109611(k)). - _Andrew Howroyd_, Dec 28 2017
%t A112022 terms = 81;
%t A112022 gf = Times @@ (1 + x^SequencePosition[ PrimeOmega[ Range[terms]], {1, _, 1|2}][[All, 1]]) + O[x]^terms;
%t A112022 CoefficientList[gf, x] (* _Jean-François Alcover_, Jul 02 2018 *)
%o A112022 (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 A112022 Cf. A112021, A112020, A109611.
%K A112022 nonn
%O A112022 0,6
%A A112022 _Reinhard Zumkeller_, Aug 26 2005