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%I #30 Sep 10 2021 07:28:33
%S 0,1,0,0,1,0,1,1,1,2,1,2,2,2,2,4,2,4,3,4,3,5,3,6,4,6,4,7,5,8,6,7,6,9,
%T 6,11,7,8,8,11,8,12,9,11,9,12,9,14,10,14,10,14,11,16,12,15,12,16,13,
%U 19,14,15,14,19,14,21,15,17,16,21,16,22,17,20,17,22,17,25,18,22,19,23,19
%N Number of ways of writing n = c1 + c2 with c1 and c2 nonprimes [=1 or composite].
%H Donovan Johnson, <a href="/A062610/b062610.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{i=1..floor(n/2)} (1 - A010051(i)) * (1 - A010051(n-i)) = Sum_{i=1..floor(n/2)} A005171(i)*A005171(n-i). - _Wesley Ivan Hurt_, Apr 08 2018
%F a(n) + A061358(n) + A062602(n) = A004526(n). - _R. J. Mathar_, Sep 10 2021
%e n = 22 has floor(n/2) = 11 partitions of form n = a+b; 3 partitions are of prime+prime [3+19 = 5+17 = 11+11], 3 partitions are of prime+nonprime [2+20 = 7+15 = 13+9], 5 partitions are of nonprime+nonprime [1+21 = 4+18 = 6+16 = 8+14 = 10+12]. So a(22) = 5.
%t Table[Count[Transpose@ {#, n - #} &@ Range[Floor[n/2]], w_ /; Times @@ Boole@ Map[! PrimeQ@ # &, w] == 1], {n, 83}] (* _Michael De Vlieger_, Jul 04 2016 *)
%Y Cf. A010051, A014092, A061358, A062602.
%K nonn,easy
%O 1,10
%A _Labos Elemer_, Jul 04 2001
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