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 A078573 #17 Sep 09 2024 02:41:03
%S A078573 2,1,2,2,1,1,2,3,1,3,1,2,2,6,2,2,4,3,1,3,2,2,4,1,2,1,3,1,1,2,4,1,2,1,
%T A078573 2,2,3,2,2,2,7,1,2,1,1,3,2,2,1,4,3,4,2,1,1,2,4,1,2,2,3,2,1,3,6,1,2,1,
%U A078573 4,1,2,1,2,5,1,7,3,1,2,1,3,3,4,5,2,2,2,2,5,2,1,1,2,3,2,1,2,3,3,2,2,1,1,1,2
%N A078573 The maximum exponent in prime factorization of the average of n-th twin prime pair.
%H A078573 Amiram Eldar, <a href="/A078573/b078573.txt">Table of n, a(n) for n = 1..10000</a>
%F A078573 a(n) = A051903(A014574(n)).
%e A078573 10th twin prime pair = (A001359(10), A006512(10)) = (107,109), hence A014574(10) = 108 = 2^2 * 3^2, therefore a(10) = 3.
%t A078573 midQ[n_] := PrimeQ[n-1] && PrimeQ[n+1]; f[n_] := Max @@ FactorInteger[n][[;;,2]]; f /@ Select[Range[5000], midQ] (* _Amiram Eldar_, Nov 03 2019 *)
%t A078573 Max[FactorInteger[Mean[#]][[All,2]]]&/@Select[Partition[Prime[Range[1000]],2,1],#[[2]] - #[[1]]==2&] (* _Harvey P. Dale_, Apr 21 2022 *)
%o A078573 (PARI) lista(pmax) = {my(prv = 2); forprime(p = 3, pmax, if(p - prv ==2, print1(vecmax(factor(p-1)[,2]), ", ")); prv = p);} \\ _Amiram Eldar_, Sep 09 2024
%Y A078573 Cf. A001359, A006512, A051903, A014574, A078570, A078572.
%K A078573 nonn
%O A078573 1,1
%A A078573 _Reinhard Zumkeller_, Nov 29 2002