%I #8 Jul 06 2024 01:40:39

%S 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 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 2,2,8,2,2,2,4,2,2,2,2,2,2,2,2,4,2,2,2

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

%H Amiram Eldar, <a href="/A374324/b374324.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A051903(A368714(n)).

%F 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 f[n_] := Module[{e = If[n == 1, 0, Max[FactorInteger[n][[;; , 2]]]]}, If[EvenQ[e], e, Nothing]]; Array[f, 350]

%o (PARI) lista(kmax) = {my(e); print1(0, ", "); for(k = 2, kmax, e = vecmax(factor(k)[, 2]); if(!(e % 2), print1(e, ", ")));}

%Y Cf. A051903, A368714.

%Y Similar sequences: A374325, A374326, A374327, A374328.

%K nonn,easy

%O 1,2

%A _Amiram Eldar_, Jul 04 2024