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 A056649 #15 Sep 28 2024 07:37:48
%S A056649 0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,2,4,6,2,2,0,0,1,2,
%T A056649 0,0,0,2,0,0,0,1,0,1,6,8,0,0,0,4,4,6,2,2,0,1,1,1,1,1,1,1,0,0,0,0,0,0,
%U A056649 0,2,0,0,0,1,0,2,4,4,0,0,4,8,2,3,6,8,4,8,2,2,4,4,8,8,0,0,0,4,2,4,3,4,2,3,4
%N A056649 a(n) = A056061(n) - A034444(A056647(n)).
%C A056649 Previous name, "Number of non-unitary square divisors of central binomial coefficient", was incorrect. See A376556 for the correct sequence with this name. - _Amiram Eldar_, Sep 28 2024
%F A056649 a(n) = A056061(n) - 2^r, where r = A001221(A000188(A001405(n))/A055229(A001405(n))).
%e A056649 a(28) = A056061(28) - A034444(A056647(28)) = A056061(28) - A034444(25) = 8 - 2 = 6.
%t A056649 A056061[n_] := Count[Divisors@Binomial[n, Floor[n/2]], d_ /; IntegerQ@Sqrt@d]; A008833[n_] := First[Select[Reverse[Divisors[n]], IntegerQ[Sqrt[#]] &, 1]]; A055229[n_] := With[{sf = Times @@ Power @@@ ({#[[1]], Mod[#[[2]], 2]} & /@ FactorInteger[n])}, GCD[sf, n/sf]];
%t A056649 Table[A056061[n] - 2^(PrimeNu[Sqrt[A008833[Binomial[n, Floor[n/2]]]]/ A055229[Binomial[n, Floor[n/2]]]]), {n, 1, 15}] (* _G. C. Greubel_, May 20 2017 *)
%Y A056649 Cf. A000188, A001221, A001405, A008833, A034444, A055229, A056056, A056057, A056059, A056061, A376556.
%K A056649 nonn
%O A056649 1,26
%A A056649 _Labos Elemer_, Aug 09 2000
%E A056649 Incorrect name replaced with a formula by _Amiram Eldar_, Sep 28 2024