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%I #16 Dec 28 2017 21:30:34
%S 0,1,1,1,2,2,3,3,4,5,6,7,9,10,12,14,17,19,23,26,30,35,40,46,52,60,67,
%T 77,87,98,111,124,140,157,175,197,219,244,272,302,336,372,412,456,503,
%U 556,613,675,742,816,896,983,1078,1180,1291,1411,1542,1683,1836,2001,2178
%N Number of partitions of n into Chen primes.
%C a(n) = A000607(n) for n <= 42.
%H Andrew Howroyd, <a href="/A112021/b112021.txt">Table of n, a(n) for n = 1..1000</a>
%F G.f.: Product_{k>=1} 1/(1 - x^A109611(k)). - _Andrew Howroyd_, Dec 28 2017
%t fQ[n_] := PrimeQ@n && (PrimeQ[n + 2] || 2 == Plus @@ Last /@ FactorInteger[n + 2]); f[n_] := Block[{c = k = 0, l = PartitionsP@n, p = Union /@ IntegerPartitions@n}, While[k++; k < l, If[Union[fQ /@ p[[k]]] == {True}, c++ ]]; c]; lst = {}; Do[ AppendTo[lst, f[n]], {n, 61}]; lst (* or *)
%t Rest@ CoefficientList[ Series[1/Times @@ (1 - x^Select[ Range@100, fQ@# &]), {x, 0, 61}], x] (* _Robert G. Wilson v_, Jun 16 2006 *)
%o (PARI)
%o ok(n)={isprime(n) && bigomega(n+2)<3}
%o {my(n=80); Vec(prod(k=1, n, if(ok(k), 1/(1-x^k) + O(x*x^n), 1))-1,-n)} \\ _Andrew Howroyd_, Dec 28 2017
%Y Cf. A112022, A101048, A109611.
%K nonn
%O 1,5
%A _Reinhard Zumkeller_, Aug 26 2005
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