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%I #36 Nov 24 2023 08:55:56
%S 0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0,1,0,1,
%T 0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,
%U 0,1,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1
%N a(n) = 1 if n is odd and squarefree, otherwise a(n) = 0.
%C Characteristic function of A056911.
%C Dirichlet inverse of A166698. - _Antti Karttunen_, Dec 19 2022
%H Antti Karttunen, <a href="/A323239/b323239.txt">Table of n, a(n) for n = 0..65537</a>
%H Jon Maiga, <a href="http://sequencedb.net/s/A323239">Computer-generated formulas for A323239</a>, Sequence Machine.
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>.
%F a(n) = A000035(n) * A008966(n).
%F For n >= 1:
%F a(n) = abs(A087003(n)) = abs(A099991(n)).
%F a(n) = A085405(A156552(n)).
%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 4/Pi^2 (A185199). - _Amiram Eldar_, Jul 24 2022
%F a(n) = A008683(n) * A166698(n).
%F From _Antti Karttunen_, Dec 19 2022: (Start)
%F Multiplicative with a(p^e) = 1 if p > 2 and e = 1, otherwise 0.
%F a(n) = A000035(n) - A353569(n).
%F (End)
%F Dirichlet g.f.: zeta(s)/(zeta(2*s)*(1+1/2^s)). - _Amiram Eldar_, Dec 27 2022
%F a(n) = Sum_{d|n} A359548(d). [From Sequence Machine] - _Antti Karttunen_, Nov 22 2023
%p f:= n -> charfcn[{true}](n::odd and numtheory:-issqrfree(n)):
%p map(f, [$0..200]); # _Robert Israel_, Jan 14 2019
%t Table[If[OddQ[n]&&SquareFreeQ[n],1,0],{n,0,120}] (* _Harvey P. Dale_, Feb 02 2021 *)
%o (PARI) A323239(n) = ((n%2) && issquarefree(n));
%o (PARI) A323239(n) = { my(f = factor(n)); prod(k=1, #f~, (f[k,1]%2)*(1==f[k,2])); }; \\ _Antti Karttunen_, Dec 19 2022
%Y Absolute values of A087003 and A099991.
%Y Cf. A000035, A008683, A008966, A056911, A085405, A156552, A166698 (Dirichlet inverse), A185199, A322810, A353481, A353569, A353627.
%Y Inverse Möbius transform of A359548.
%K nonn,mult
%O 0
%A _Antti Karttunen_, Jan 12 2019
%E Keyword:mult added by _Antti Karttunen_, Dec 19 2022
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