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A375360 The maximum exponent in the prime factorization of the smallest exponentially odd number that is divisible by n.

%I A375360 #9 Aug 13 2024 09:10:55
%S A375360 0,1,1,3,1,1,1,3,3,1,1,3,1,1,1,5,1,3,1,3,1,1,1,3,3,1,3,3,1,1,1,5,1,1,
%T A375360 1,3,1,1,1,3,1,1,1,3,3,1,1,5,3,3,1,3,1,3,1,3,1,1,1,3,1,1,3,7,1,1,1,3,
%U A375360 1,1,1,3,1,1,3,3,1,1,1,5,5,1,1,3,1,1,1,3,1,3,1,3,1,1,1,5,1,3,3,3,1,1,1,3,1
%N A375360 The maximum exponent in the prime factorization of the smallest exponentially odd number that is divisible by n.
%C A375360 Differs from A365331 at n = 1, 36, 72, 100, ... .
%H A375360 Amiram Eldar, <a href="/A375360/b375360.txt">Table of n, a(n) for n = 1..10000</a>
%H A375360 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%F A375360 a(n) = A051903(A356191(n)).
%F A375360 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 + 2 * Sum{k>=1} (1 - 1/zeta(2*k)) = 1.98112786070359477197... .
%t A375360 a[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, Max[(If[OddQ[#], #, # + 1]) & /@ e]]; a[1] = 0; Array[a, 100]
%o A375360 (PARI) a(n) = if(n == 1, 0, vecmax(apply(x -> if(x % 2, x, x+1), factor(n)[,2])));
%Y A375360 Cf. A051903, A356191, A365331, A372601, A375359.
%K A375360 nonn,easy
%O A375360 1,4
%A A375360 _Amiram Eldar_, Aug 13 2024