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%I #27 Sep 08 2022 08:45:46
%S 1,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,
%T 0,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,
%U 0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,1,0,1,0,0
%N a(n) = 1 if n is relatively prime to 30 else 0.
%H Antti Karttunen, <a href="/A162289/b162289.txt">Table of n, a(n) for n = 1..65537</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F Euler transform of length 30 sequence [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1].
%F Moebius transform is length 30 sequence [1, -1, -1, 0, -1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1].
%F a(n) is multiplicative with a(2^e) = a(3^e) = a(5^e) = 0^e, a(p^e) = 1 if p>5.
%F a(n) = a(n + 30) = a(-n) for all n in Z.
%F G.f.: x * (1 + x^6) * (1 + x^10) * (1 + x^12) / (1 - x^30).
%F Dirichlet g.f.: zeta(s)*(1-1/2^s)*(1-1/3^s)*(1-1/5^s). - _R. J. Mathar_, Jun 01 2011
%F Asymptotic mean: lim_{n->oo} (1/n) * Sum_{k=1..n} = 4/15. - _Amiram Eldar_, Dec 06 2020
%e G.f. = x + x^7 + x^11 + x^13 + x^17 + x^19 + x^23 + x^29 + x^31 + x^37 + ...
%t Boole[CoprimeQ[Range[110],30]] (* _Harvey P. Dale_, Jul 11 2017 *)
%o (PARI) {a(n) = 1 == gcd(30, n)};
%o (PARI) x='x+O('x^100); Vec(x*(1+x^6)*(1+x^10)*(1+x^12)/(1-x^30)) \\ _G. C. Greubel_, Sep 25 2018
%o (Magma) m:=100; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1+x^6)*(1+x^10)*(1+x^12)/(1-x^30))); // _G. C. Greubel_, Sep 25 2018
%K nonn,mult
%O 1,1
%A _Michael Somos_, Jun 29 2009
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