A354354 a(n) = 1 if n is neither a multiple of 2 nor 3, and otherwise 0.

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, 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, 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, 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, 0, 1, 0

Offset

0

Comments

Period 6: repeat [0, 1, 0, 0, 0, 1].

Links

Antti Karttunen, Table of n, a(n) for n = 0..65537

Index entries for characteristic functions.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).

Formula

Fully multiplicative with a(2^e) = a(3^e) = 0, and for p > 3, a(p^e) = 1.

a(n) = 1 if gcd(n,6) == 1, otherwise 0.

a(n) = abs(A109017(n)) = abs(A110161(n)) = abs(A134667(n)) = abs(A322796(n)).

a(n) = A120325(n+3), and for n >= 1, a(n) = A232991(n-1).

For n > 1, a(n) * A065333(n) = 0.

G.f.: x*(1 + x^4)/((1 - x)*(1 + x)*(1 - x + x^2)*(1 + x + x^2)). - Stefano Spezia, May 25 2022

Dirichlet g.f.: zeta(s)*(1-1/2^s)*(1-1/3^s). - Amiram Eldar, Dec 27 2022

Mathematica

a[n_] := If[GCD[n, 6] == 1, 1, 0]; Array[a, 100, 0] (* Amiram Eldar, Dec 27 2022 *)

Prog

(PARI) A354354(n) = ((n%2)&&(n%3));
(PARI) A354354(n) = (1==gcd(n, 6));
(PARI) A354354(n) = if(!n, 0, my(f=factor(n)); prod(k=1, #f~, (f[k, 1]>3)));
(Python)
def A354354(n): return int(not n % 6 & 3 ^ 1) # Chai Wah Wu, May 25 2022

Crossrefs

Characteristic function of A007310.

Absolute values of the following sequences: A109017, A110161, A134667, A322796.

Essentially same as sequences A120325 and A232991, but shifted.

Cf. A089128.

Cf. also A065333.

Sequence in context: A109017 A110161 A134667 * A117943 A285969 A189664

Adjacent sequences: A354351 A354352 A354353 * A354355 A354356 A354357

Keyword

nonn,easy,mult

Author

Antti Karttunen, May 25 2022

Status

approved