%I #11 Jun 28 2024 04:25:50
%S 1,0,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,
%T 1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,1,0,0,1,0,1,0,0,1,1,0,1,0,
%U 0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1
%N a(n) = 1 if n is a non-multiple of 3 whose 2-adic valuation is a multiple of 3, otherwise 0.
%H Antti Karttunen, <a href="/A374043/b374043.txt">Table of n, a(n) for n = 1..100000</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>.
%F Multiplicative with a(2^e) = A079978(e), a(3^e) = 0 for e >= 1, and a(p^e) = 1 for all primes p > 3, and e >= 1.
%F a(n) = A011655(n) * A373157(n).
%F From _Amiram Eldar_, Jun 28 2024: (Start)
%F Dirichlet g.f.: zeta(s) * (1 - 1/3^s) / (1 + 1/2^s + 1/4^s).
%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 8/21. (End)
%t a[n_] := If[!Divisible[n, 3] && Divisible[IntegerExponent[n, 2], 3], 1, 0]; Array[a, 100] (* _Amiram Eldar_, Jun 28 2024 *)
%o (PARI) A374043(n) = (n%3 && !(valuation(n,2)%3));
%Y Characteristic function of A374044.
%Y Cf. A011655, A373157.
%K nonn,mult,easy
%O 1
%A _Antti Karttunen_, Jun 27 2024