This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A224708 #37 Feb 01 2021 18:17:38
%S A224708 0,0,0,0,0,0,0,1,0,1,0,2,1,2,1,3,1,4,2,4,2,4,2,6,3,5,3,6,4,8,5,7,5,8,
%T A224708 5,10,6,8,7,10,7,12,8,11,8,11,8,14,9,13,9,13,10,16,11,14,11,15,12,19,
%U A224708 13,15,13,18,13,20,14,17,15,20,15,22,16,20,16,21
%N A224708 The number of unordered partitions {a,b} of n such that a and b are composite.
%C A224708 For n > 11, a(n) > 0. - _Geoffrey Critzer_, Jan 31 2015
%C A224708 Last occurrence of n is a(A014092(n+4)). - _Anthony Browne_, May 25 2016
%H A224708 J. Stauduhar, <a href="/A224708/b224708.txt">Table of n, a(n) for n = 1..10000</a>
%F A224708 a(2*n) - a(2*n+1) + A010051(n) = A045917(n). - _Anthony Browne_, May 03 2016
%F A224708 a(A014092(n+4)) = n. - _Anthony Browne_, May 25 2016
%e A224708 For n=8, in the set {{7,1},{6,2},{5,3},{4,4}}, {4,4} is the only partition {a,b} where a and b are both composite, so a(8)=1.
%e A224708 For n=12, we have partitions {8,4} and {6,6}, so a(12)=2.
%t A224708 nn = 76; Rest[Transpose[CoefficientList[Series[Product[1/(1 - y x^i), {i, Select[Range[2, nn], ! PrimeQ[#] &]}], {x,0,nn}], {x, y}]][[3]]] (* _Geoffrey Critzer_, Jan 31 2015 *)
%t A224708 f[n_] := Count[ PrimeQ@ Rest@ IntegerPartitions[ n, {2}], {False, False}]; Array[f, 76] (* _Robert G. Wilson v_, Feb 04 2015 *)
%Y A224708 Cf. A010051, A014092, A045917, A066247.
%K A224708 nonn,easy
%O A224708 1,12
%A A224708 _J. Stauduhar_, Apr 16 2013