A374043 a(n) = 1 if n is a non-multiple of 3 whose 2-adic valuation is a multiple of 3, otherwise 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, 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, 1, 1, 0, 1, 0, 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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions.

Formula

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.

a(n) = A011655(n) * A373157(n).

From Amiram Eldar, Jun 28 2024: (Start)

Dirichlet g.f.: zeta(s) * (1 - 1/3^s) / (1 + 1/2^s + 1/4^s).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 8/21. (End)

Mathematica

a[n_] := If[!Divisible[n, 3] && Divisible[IntegerExponent[n, 2], 3], 1, 0]; Array[a, 100] (* Amiram Eldar, Jun 28 2024 *)

Prog

(PARI) A374043(n) = (n%3 && !(valuation(n, 2)%3));

Crossrefs

Characteristic function of A374044.

Cf. A011655, A373157.

Sequence in context: A266444 A267679 A267868 * A374041 A288733 A095111

Adjacent sequences: A374040 A374041 A374042 * A374044 A374045 A374046

Keyword

nonn,mult,easy,new

Author

Antti Karttunen, Jun 27 2024

Status

approved