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 A056676 #17 Oct 04 2024 10:02:09
%S A056676 0,0,0,0,0,2,0,0,4,6,0,8,8,8,8,16,0,16,0,16,32,32,0,32,48,48,56,56,96,
%T A056676 96,64,128,128,192,256,384,384,384,512,768,512,512,512,512,448,448,
%U A056676 768,896,896,896,896,896,768,768,2048,2048,4096,4096,2048,2048,2048,2048
%N A056676 Number of non-unitary but squarefree divisors of binomial(n,floor(n/2)). Also number of nonsquarefree but unitary divisors of binomial(n,floor(n/2)).
%H A056676 Amiram Eldar, <a href="/A056676/b056676.txt">Table of n, a(n) for n = 1..1000</a>
%F A056676 a(n) = A039593(n) - A000005(A055231(x)) = A039593(n) - A000005(A007913(x)/A055229(x)), where x = A001405(n) = binomial(n, floor(n/2)).
%F A056676 a(n) = A039593(n) - A056673(n). - _Sean A. Irvine_, May 02 2022
%F A056676 a(n) = A056674(A001405(n)). - _Amiram Eldar_, Oct 04 2024
%e A056676 For n = 14, binomial(14,7) = 3432 has 32 divisors, 16 unitary, 16 squarefree. The size of overlap is 8. The complementary parts are: non-unitary/squarefree set ={2,6,22,26,66,78,286,828}, while the unitary/not squarefree set of equal size is {8,24,88,104,264,312,1144,3432}. So a(14) = 8.
%t A056676 f[p_, e_] := If[e == 1, 2, 1]; a[1] = 0; a[n_] := 2^Length[fct = FactorInteger[Binomial[n, Floor[n/2]]]] - Times @@ f @@@ fct; Array[a, 100] (* _Amiram Eldar_, Oct 04 2024 *)
%o A056676 (PARI) a(n) = {my(f = factor(binomial(n, n\2)), e = f[, 2]); 2^omega(f) - prod(i = 1, #e, if(e[i] == 1, 2, 1)); } \\ _Amiram Eldar_, Oct 04 2024
%Y A056676 Cf. A039593, A000005, A055231, A007913, A055229, A001405, A056673, A056674.
%K A056676 nonn
%O A056676 1,6
%A A056676 _Labos Elemer_, Aug 10 2000