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A187074 a(n) = 0 if and only if n is of the form 3*k or 4*k + 2, otherwise a(n) = 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, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..105.

Michael Somos, Rational Function Multiplicative Coefficients

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

EXAMPLE

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

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 *)

PROG

(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] )};

CROSSREFS

Sequence in context: A028863 A089012 A083035 * A188398 A288929 A285083

Adjacent sequences:  A187071 A187072 A187073 * A187075 A187076 A187077

KEYWORD

nonn,mult

AUTHOR

Michael Somos, Mar 07 2011

STATUS

approved

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Last modified April 18 10:21 EDT 2021. Contains 343087 sequences. (Running on oeis4.)