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 A069785 #12 Dec 02 2023 09:12:38
%S A069785 1,1,1,1,1,15,15,3,5,135,135,99,99,9,63,21,21,459,459,135,19,15,15,15,
%T A069785 21,189,189,585,585,18225,18225,675,15,135,891,8505,25515,81,81,7695,
%U A069785 7695,1575,1575,4725,6615,40635,40635,945,1215,3645,3645,151875,151875
%N A069785 a(n) = A061680(n!).
%H A069785 Amiram Eldar, <a href="/A069785/b069785.txt">Table of n, a(n) for n = 1..1000</a>
%F A069785 a(n) = A061680(A000142(n)). - _Amiram Eldar_, Dec 02 2023
%e A069785 Observe cases when consecutive terms are equal: n={1,2,3,4,6,10,...,78,80,82,88,96}.
%t A069785 a[n_] := Module[{e = FactorInteger[n!][[;;, 2]]}, GCD[Times @@ (2*e+1), Times @@ (e+1)]]; Array[a, 100] (* _Amiram Eldar_, Dec 02 2023 *)
%o A069785 (PARI) a(n) = {my(e = factor(n!)[,2]); gcd(vecprod(apply(x -> 2*x+1, e)), vecprod(apply(x -> x+1, e)));} \\ _Amiram Eldar_, Dec 02 2023
%Y A069785 Cf. A000005, A000142, A061680, A061701, A048691, A069780, A069781, A069782, A069783, A069784.
%K A069785 easy,nonn
%O A069785 1,6
%A A069785 _Labos Elemer_, Apr 09 2002