A187074 a(n) = 0 if and only if n is of the form 3*k or 4*k + 2, otherwise a(n) = 1.

1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0

Offset: 1

Author

Michael Somos, Mar 07 2011

Keywords

• nonn
• mult

Comments

Characteristic function of A359380, numbers that are neither multiples of 3 nor of the form 4u+2. - Antti Karttunen, Dec 31 2022

Examples

			x + x^4 + x^5 + x^7 + x^8 + x^11 + x^13 + x^16 + x^17 + x^19 + x^20 + ...
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000
• Michael Somos, Rational Function Multiplicative Coefficients
• Index entries for characteristic functions

Crossrefs

Characteristic function of A359380.

Cf. A000661, A011655, A152822, A359374, A359422 (Dirichlet inverse).

Programs

Mathematica

PadRight[{}, 120, {1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0}] (* or *)
Table[If[MemberQ[{0, 2, 3, 6, 9, 10}, Mod[n, 12]], 0, 1], {n, 120}] (* or *)
Table[Boole@ Or[CoprimeQ[n, 12], MemberQ[{4, 8}, Mod[n, 12]]], {n, 120}] (* or *)
Rest@ CoefficientList[Series[x (1 + x^4) (1 + x^3 + x^6)/(1 - x^12), {x, 0, 121}], x] (* Michael De Vlieger, Jul 16 2016 *)
Table[Which[Mod[n,3]==0,0,Mod[n,4]==2,0,True,1],{n,120}] (* Harvey P. Dale, Aug 02 2021 *)

PARI

{a(n) = [0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1][n%12 + 1]};

PARI

{a(n) = n = abs(n); sumdiv( 12, k, (n%k == 0) * [ 1, -1, -1, 1, 0, 1, 0, 0, 0, 0, 0, -1][k] )};

PARI

A187074(n) = ((n%3)&&(2!=(n%4))); \\ Antti Karttunen, Dec 31 2022

Formula

Euler transform of length 12 sequence [0, 0, 1, 1, 0, 0, 0, -1, -1, 0, 0, 1].

Moebius transform is length 12 sequence [1, -1, -1, 1, 0, 1, 0, 0, 0, 0, 0, -1].

a(n) is multiplicative with a(2^e) = 1 except a(2) = 0, a(3^e) = 0^e, a(p^e) = 1 if p>3.

G.f.: x * (1 + x^4) * (1 + x^3 + x^6) / (1 - x^12). a(n + 12) = a(-n) = a(n). a(3*n) = a(4*n + 2) = 0.

Dirichlet g.f. zeta(s)*(1-3^(-s))*(1+4^(-s)-2^(-s)). - R. J. Mathar, Mar 31 2011

a(n+5) = A000661(n)(mod 2). - John M. Campbell, Jul 15 2016

a(n) = A011655(n) * A152822(n). - Antti Karttunen, Dec 31 2022