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 A368821 #3 Jan 06 2024 23:59:18
%S A368821 0,1,2,1,0,0,0,0,2,4,2,0,2,2,0,1,2,1,2,4,2,0,0,1,2,4,2,0,0,2,0,2,2,0,
%T A368821 0,3,2,2,0,0,2,4,0,2,2,0,0,5,2,0,0,2,0,2,0,0,2,4,0,2,2,2,0,4,2,0,0,4,
%U A368821 2,0,0,3,2,4,0,2,0,2,0,5,4,2,0,4,2,2,0,2,4,4,0,6,2,0,0,10,4
%N A368821 Number of compositions of n into 2 refactorable parts.
%H A368821 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A368821 a(n) = Sum_{k=1..n-1} c(k) * c(n-k), where c = A336040.
%e A368821 a(10) = 4. There are 4 ordered ways to write 10 as the sum of two refactorable numbers: 1 + 9 = 2 + 8 = 8 + 2 = 9 + 1.
%e A368821 a(36) = 3. There are 3 ordered ways to write 36 as the sum of two refactorable numbers: 12 + 24 = 18 + 18 = 24 + 12.
%t A368821 Table[Sum[(1 - Ceiling[k/DivisorSigma[0, k]] + Floor[k/DivisorSigma[0, k]]) (1 - Ceiling[(n - k)/DivisorSigma[0, (n - k)]] + Floor[(n - k)/DivisorSigma[0, (n - k)]]), {k, n - 1}], {n, 100}]
%Y A368821 Cf. A033950, A336040.
%K A368821 nonn,easy
%O A368821 1,3
%A A368821 _Wesley Ivan Hurt_, Jan 06 2024