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 A375039 #8 Jul 29 2024 06:17:56
%S A375039 0,1,1,1,2,1,1,1,1,1,1,1,2,3,1,1,1,1,1,1,1,1,2,1,2,1,1,1,1,1,1,2,1,1,
%T A375039 1,1,1,2,1,1,4,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,2,1,2,1,3,1,1,1,1,3,
%U A375039 1,1,1,1,1,2,1,1,2,1,1,1,1,1,1,1,2,2,1,2,1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,2,1
%N A375039 The maximum exponent in the prime factorization of 2*n-1.
%H A375039 Amiram Eldar, <a href="/A375039/b375039.txt">Table of n, a(n) for n = 1..10000</a>
%H A375039 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%F A375039 a(n) = A051903(2*n-1).
%F A375039 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 + Sum_{k>=2} (1 - 1/((1-1/2^k) * zeta(k))) = 1.25979668632898014495... .
%t A375039 a[n_] := Max[FactorInteger[2*n - 1][[;; , 2]]]; a[1] = 0; Array[a, 100]
%o A375039 (PARI) a(n) = if(n == 1, 0, vecmax(factor(2*n-1)[,2]));
%Y A375039 Bisection of A051903.
%Y A375039 Cf. A033150, A375040.
%K A375039 nonn,easy
%O A375039 1,5
%A A375039 _Amiram Eldar_, Jul 28 2024