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%I #7 Jul 29 2024 06:17:50
%S 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 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 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 The maximum exponent in the prime factorization of 2*n.
%H Amiram Eldar, <a href="/A375040/b375040.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%F a(n) = A051903(2*n).
%F 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 a[n_] := Max[FactorInteger[2*n][[;; , 2]]]; Array[a, 100]
%o (PARI) a(n) = vecmax(factor(2*n)[,2]);
%Y Bisection of A051903.
%Y Cf. A033150, A375039.
%K nonn,easy
%O 1,2
%A _Amiram Eldar_, Jul 28 2024
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