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%I #36 Jan 05 2023 09:14:58
%S 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,
%T 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,
%U 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
%N a(n) = 0 if and only if n is of the form 3*k or 4*k + 2, otherwise a(n) = 1.
%C Characteristic function of A359380, numbers that are neither multiples of 3 nor of the form 4u+2. - _Antti Karttunen_, Dec 31 2022
%H Antti Karttunen, <a href="/A187074/b187074.txt">Table of n, a(n) for n = 1..100000</a>
%H Michael Somos, <a href="http://grail.eecs.csuohio.edu/~somos/rfmc.html">Rational Function Multiplicative Coefficients</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F Euler transform of length 12 sequence [0, 0, 1, 1, 0, 0, 0, -1, -1, 0, 0, 1].
%F Moebius transform is length 12 sequence [1, -1, -1, 1, 0, 1, 0, 0, 0, 0, 0, -1].
%F 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.
%F 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.
%F Dirichlet g.f. zeta(s)*(1-3^(-s))*(1+4^(-s)-2^(-s)). - _R. J. Mathar_, Mar 31 2011
%F a(n+5) = A000661(n)(mod 2). - _John M. Campbell_, Jul 15 2016
%F a(n) = A011655(n) * A152822(n). - _Antti Karttunen_, Dec 31 2022
%e x + x^4 + x^5 + x^7 + x^8 + x^11 + x^13 + x^16 + x^17 + x^19 + x^20 + ...
%t PadRight[{}, 120, {1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0}] (* or *)
%t Table[If[MemberQ[{0, 2, 3, 6, 9, 10}, Mod[n, 12]], 0, 1], {n, 120}] (* or *)
%t Table[Boole@ Or[CoprimeQ[n, 12], MemberQ[{4, 8}, Mod[n, 12]]], {n, 120}] (* or *)
%t 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 *)
%t Table[Which[Mod[n,3]==0,0,Mod[n,4]==2,0,True,1],{n,120}] (* _Harvey P. Dale_, Aug 02 2021 *)
%o (PARI) {a(n) = [0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1][n%12 + 1]};
%o (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] )};
%o (PARI) A187074(n) = ((n%3)&&(2!=(n%4))); \\ _Antti Karttunen_, Dec 31 2022
%Y Characteristic function of A359380.
%Y Cf. A000661, A011655, A152822, A359374, A359422 (Dirichlet inverse).
%K nonn,mult
%O 1,1
%A _Michael Somos_, Mar 07 2011
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