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A372601 The maximal exponent in the prime factorization of the largest exponentially odd divisor of n.

%I A372601 #11 May 08 2024 08:53:06
%S A372601 0,1,1,1,1,1,1,3,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,3,1,1,3,1,1,1,1,5,1,1,
%T A372601 1,1,1,1,1,3,1,1,1,1,1,1,1,3,1,1,1,1,1,3,1,3,1,1,1,1,1,1,1,5,1,1,1,1,
%U A372601 1,1,1,3,1,1,1,1,1,1,1,3,3,1,1,1,1,1,1
%N A372601 The maximal exponent in the prime factorization of the largest exponentially odd divisor of n.
%C A372601 First differs from A331273 at n = 64.
%C A372601 Differs from A363332 at n = 1, 216, 432, 648, 864, 1000, ... .
%H A372601 Amiram Eldar, <a href="/A372601/b372601.txt">Table of n, a(n) for n = 1..10000</a>
%F A372601 a(n) = A051903(A350390(n)).
%F A372601 a(n) = A109613(A051903(n)-1) for n >= 2.
%F A372601 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 + 2 * Sum_{i>=1} (1 - (1/zeta(2*i+1))) = 1.42929441950714075659... .
%t A372601 f[n_] := n - If[EvenQ[n], 1, 0]; a[n_] := f[Max[FactorInteger[n][[;; , 2]]]]; a[1] = 0; Array[a, 100]
%o A372601 (PARI) s(n) = (n+1) \ 2 * 2 - 1;
%o A372601 a(n) = if(n>1, s(vecmax(factor(n)[,2])), 0);
%Y A372601 Cf. A051903, A109613, A350390, A368711.
%Y A372601 Cf. A331273, A363332.
%Y A372601 Similar sequences: A007424, A368781, A372602, A372603, A372604.
%K A372601 nonn,easy
%O A372601 1,8
%A A372601 _Amiram Eldar_, May 07 2024