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 A339927 #6 Jul 02 2022 15:42:31
%S A339927 0,0,0,0,0,0,0,1,0,0,0,1,1,1,0,2,0,2,0,2,1,1,1,2,1,0,1,2,3,3,1,4,1,2,
%T A339927 2,4,2,1,1,4,4,3,3,4,2,2,3,7,4,3,0,4,4,5,2,5,3,1,3,7,6,3,3,6,6,5,3,6,
%U A339927 2,6,3,11,7,2,3,4,6,5,5,8,3,4,5,10,4,4,3,7,5,7,7,7
%N A339927 Number of partitions of n into two composite parts with the same number of divisors.
%H A339927 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A339927 a(n) = Sum_{k=2..floor(n/2)} [d(k) = d(n-k)] * c(k) * c(n-k), where [ ] is the Iverson bracket, d(n) is the number of divisors of n (A000005), and c is the characteristic function of composite numbers (A066247).
%e A339927 a(18) = 2; 18 has two partitions into two composite parts that have the same number of divisors, (10,8) and (9,9).
%t A339927 Table[Sum[KroneckerDelta[DivisorSigma[0, i], DivisorSigma[0, n - i]] (1 - PrimePi[i] + PrimePi[i - 1]) (1 - PrimePi[n - i] + PrimePi[n - i - 1]), {i, 2, Floor[n/2]}], {n, 100}]
%t A339927 Table[Count[IntegerPartitions[n,{2}],_?(AllTrue[#,CompositeQ]&&Length[Union[ DivisorSigma[ 0,#]]]==1&)],{n,100}] (* _Harvey P. Dale_, Jul 02 2022 *)
%Y A339927 Cf. A000005, A066247, A224708.
%K A339927 nonn
%O A339927 1,16
%A A339927 _Wesley Ivan Hurt_, Dec 23 2020