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%I #24 Mar 28 2023 12:37:34
%S 0,1,1,1,2,2,3,2,3,3,3,3,4,3,4,4,5,4,5,4,6,5,6,6,6,6,7,5,8,5,8,5,10,6,
%T 8,8,10,6,11,5,12,7,12,7,13,7,14,9,13,9,15,7,17,8,15,8,17,7,17,10,18,
%U 9,20,8,21,11,21,8,21,7,23,11,23,11,23,10,28,12,25,11,26
%N Number of partitions of n into sum of at most three primes.
%C a(n) = A010051(n) + A061358(n) + A068307(n). [From _Reinhard Zumkeller_, Aug 08 2009]
%H T. D. Noe, <a href="/A071335/b071335.txt">Table of n, a(n) for n=1..10000</a>
%e a(21)=6 as 21 = 2+19 = 2+2+17 = 3+5+13 = 3+7+11 = 5+5+11 = 7+7+7.
%t goldbachcount[p1_] := (parts=IntegerPartitions[p1, 3]; count=0; n=1;
%t While[n<=Length[parts], If[Intersection[Flatten[PrimeQ[parts[[n]]]]][[1]]==True, count++]; n++]; count); Table[goldbachcount[i], {i, 1, 100}] (* _Frank M Jackson_, Mar 25 2013 *)
%t Table[Length[Select[IntegerPartitions[n,3],AllTrue[#,PrimeQ]&]],{n,90}] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Oct 21 2016 *)
%Y Cf. A002375, A068307, A025583.
%K nonn,look
%O 1,5
%A _Reinhard Zumkeller_, May 19 2002
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