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A374324 The maximal exponent in the prime factorization of the numbers whose maximal exponent in their prime factorization is even.

%I A374324 #8 Jul 06 2024 01:40:39
%S A374324 0,2,2,2,4,2,2,2,2,2,2,2,4,2,2,2,2,2,6,2,2,2,4,4,2,2,2,2,2,2,4,2,2,2,
%T A374324 2,2,2,2,4,2,2,2,2,2,4,2,2,2,2,2,4,2,2,6,2,2,2,2,4,2,2,2,2,2,2,4,2,2,
%U A374324 2,2,8,2,2,2,4,2,2,2,2,2,2,2,2,4,2,2,2
%N A374324 The maximal exponent in the prime factorization of the numbers whose maximal exponent in their prime factorization is even.
%H A374324 Amiram Eldar, <a href="/A374324/b374324.txt">Table of n, a(n) for n = 1..10000</a>
%F A374324 a(n) = A051903(A368714(n)).
%F A374324 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} (2*k * (1/zeta(2*k+1) - 1/zeta(2*k))) / Sum_{k>=2} (-1)^k * (1 - 1/zeta(k)) = 2.48584683692026915946... .
%t A374324 f[n_] := Module[{e = If[n == 1, 0, Max[FactorInteger[n][[;; , 2]]]]}, If[EvenQ[e], e, Nothing]]; Array[f, 350]
%o A374324 (PARI) lista(kmax) = {my(e); print1(0, ", "); for(k = 2, kmax, e = vecmax(factor(k)[, 2]); if(!(e % 2), print1(e, ", ")));}
%Y A374324 Cf. A051903, A368714.
%Y A374324 Similar sequences: A374325, A374326, A374327, A374328.
%K A374324 nonn,easy
%O A374324 1,2
%A A374324 _Amiram Eldar_, Jul 04 2024