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%I #22 May 08 2022 05:26:01
%S 0,0,0,0,0,0,0,1,1,2,2,2,3,5,3,5,3,6,7,8,4,8,6,10,8,10,7,14,10,16,12,
%T 14,9,16,14,17,12,17,16,25,15,20,20,23,20,25,20,28,22,25,23,30,23,31,
%U 28,33,28,35,32,36,30,33,32,44,35,34,37,42,43,49,39,42,42,44,49,49,40,45,51
%N Number of partitions of n into two primes and a semiprime.
%H Alois P. Heinz, <a href="/A133850/b133850.txt">Table of n, a(n) for n = 1..5000</a>
%e Examples:
%e n a(n)
%e 0-7 0
%e 8 1 2+2+4,
%e 9 1 2+3+4,
%e 10 2 2+2+6 = 3+3+4,
%e 11 2 2+3+6 = 2+5+4,
%e 12 2 3+3+6 = 3+5+4,
%e 13 3 2+2+9 = 2+5+6 = 2+7+4,
%e 14 5 2+2+10 = 2+3+9 = 3+5+6 = 3+7+4 = 5+5+4,
%e 15 3 2+3+10 = 2+7+6 = 3+3+9,
%e 16 5 2+5+9 = 3+3+10 = 3+7+6 = 5+5+6 = 5+7+4,
%e 17 3 2+5+10 = 2+11+4 = 3+5+9,
%e 18 6 2+2+14 = 2+7+9 = 3+5+10 = 3+11+4 = 5+7+6 = 7+7+4, etc.
%t semiPrimeQ[x_] := Plus @@ Last /@ FactorInteger[x] == 2; f[n_] := Block[{c = 0, i = j = 1, p = PrimePi[(n - 4)/2]}, While[i < p + 1, j = i; q = PrimePi[n - 4 - Prime@i]; While[j < q + 1, If[semiPrimeQ[n - Prime@i - Prime@j], c++ ]; j++ ]; i++ ]; c]; Array[f, 70] (* _Robert G. Wilson v_ *)
%Y Cf. A000040, A001358.
%K nonn
%O 1,10
%A _Jonathan Vos Post_, Jan 21 2008
%E More terms from _Robert G. Wilson v_, Jan 21 2008
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