%I A112021
%S A112021 0,1,1,1,2,2,3,3,4,5,6,7,9,10,12,14,17,19,23,26,30,35,40,46,52,60,67,77,
%T A112021 87,98,111,124,140,157,175,197,219,244,272,302,336,372,412,456,503,556,
%U A112021 613,675,742,816,896,983,1078,1180,1291,1411,1542,1683,1836,2001,2178
%N A112021 Number of partitions of n into Chen primes.
%C A112021 a(n) = A000607 for n <= 42.
%t A112021 (* first *) Needs["DiscreteMath`Combinatorica`"] (* then *) fQ[n_] := 
               PrimeQ@n && (PrimeQ[n + 2] || 2 == Plus @@ Last /@ FactorInteger[n 
               + 2]); f[n_] := Block[{c = k = 0, l = PartitionsP@n, p = Union /@ 
               Partitions@n}, While[k++; k < l, If[Union[fQ /@ p[[k]]] == {True}, 
               c++ ]]; c]; lst = {}; Do[ AppendTo[lst, f[n]], {n, 61}]; lst (* or 
               *)
%t A112021 Rest@ CoefficientList[ Series[1/Times @@ (1 - x^Select[ Range@100, fQ@# 
               &]), {x, 0, 61}], x] (from Robert G. Wilson v (rgwv(at)rgwv.com), 
               Jun 16 2006)
%Y A112021 Cf. A112022, A101048, A109611.
%Y A112021 Sequence in context: A027583 A029022 A140953 this_sequence A000607 A114372 
               A046676
%Y A112021 Adjacent sequences: A112018 A112019 A112020 this_sequence A112022 A112023 
               A112024
%K A112021 nonn
%O A112021 1,5
%A A112021 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 26 2005