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 A375040 #7 Jul 29 2024 06:17:50
%S A375040 1,2,1,3,1,2,1,4,2,2,1,3,1,2,1,5,1,2,1,3,1,2,1,4,2,2,3,3,1,2,1,6,1,2,
%T A375040 1,3,1,2,1,4,1,2,1,3,2,2,1,5,2,2,1,3,1,3,1,4,1,2,1,3,1,2,2,7,1,2,1,3,
%U A375040 1,2,1,4,1,2,2,3,1,2,1,5,4,2,1,3,1,2,1,4,1,2,1,3,1,2,1,6,1,2,2,3,1,2,1,4,1
%N A375040 The maximum exponent in the prime factorization of 2*n.
%H A375040 Amiram Eldar, <a href="/A375040/b375040.txt">Table of n, a(n) for n = 1..10000</a>
%H A375040 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%F A375040 a(n) = A051903(2*n).
%F A375040 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 + Sum_{k>=2} (1 - (2^k-2)/((2^k-1)*zeta(k))) = 2.15062559388175538361... .
%t A375040 a[n_] := Max[FactorInteger[2*n][[;; , 2]]]; Array[a, 100]
%o A375040 (PARI) a(n) = vecmax(factor(2*n)[,2]);
%Y A375040 Bisection of A051903.
%Y A375040 Cf. A033150, A375039.
%K A375040 nonn,easy
%O A375040 1,2
%A A375040 _Amiram Eldar_, Jul 28 2024