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%I #12 Mar 27 2013 14:27:42
%S 1,1,2,1,2,2,2,3,2,3,2,3,3,4,3,4,3,5,5,6,5,5,5,6,6,6,5,4,6,6,9,7,7,6,
%T 8,7,10,6,8,5,10,8,12,9,10,7,13,9,14,10,12,7,15,9,17,9,13,6,17,10,21,
%U 10,15,8,19,11,22,9,16,8,24,12,25,12,19,10,26,12
%N Number of partitions of n into at most three distinct primes (including 1).
%C Using {1 union primes} as the base, the above sequence relies on the strong Goldbach's conjecture that any positive integer is the sum of at most three distinct terms.
%H T. D. Noe, <a href="/A218469/b218469.txt">Table of n, a(n) for n = 1..1000</a>
%e a(21)=5 as 21 = 2+19 = 1+3+17 = 1+7+13 = 3+5+13 = 3+7+11.
%t primeQ[p0_] := If[p0==1, True, PrimeQ[p0]]; SetAttributes[primeQ, Listable]; goldbachcount[p1_] := (parts=IntegerPartitions[p1, 3]; count=0; n=1; While[n<=Length[parts], If[Intersection[Flatten[primeQ
%t [parts[[n]]]]][[1]]&&Total[Intersection[parts[[n]]]]==Total[parts
%t [[1]]], count++]; n++]; count); Table[goldbachcount[i], {i, 1, 100}]
%Y Cf. A002375, A025583, A068307, A071335, A185101, A218007.
%K nonn
%O 1,3
%A _Frank M Jackson_, Mar 26 2013
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