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%I #21 Jan 24 2023 02:50:51
%S 0,0,0,1,0,0,0,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0,
%T 0,0,0,0,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0,0,1,
%U 0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0,0,1,0,1,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1
%N a(n) = (A166486(n)+A353627(n)) mod 2.
%H Antti Karttunen, <a href="/A359467/b359467.txt">Table of n, a(n) for n = 1..100000</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>.
%F a(n) = (A166486(n)+A355689(n)) mod 2 = (A353627(n)+A358839(n)) mod 2.
%F a(n) = A342419(n) mod 2.
%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 3/4 - 4/Pi^2 = 0.344715... . - _Amiram Eldar_, Jan 24 2023
%t a[n_] := Module[{e = IntegerExponent[n, 2], o}, o = n/2^e; sqf = SquareFreeQ[o]; If[(e > 1 && sqf) || (e < 2 && ! sqf), 1, 0]]; Array[a, 100] (* _Amiram Eldar_, Jan 24 2023 *)
%o (PARI) A359467(n) = (((!(n%4))&&issquarefree(n>>valuation(n, 2))) + ((n%4)&&!issquarefree(n)));
%o (PARI)
%o A166486(n) = !!(n%4);
%o A355689(n) = { my(f = factor(n)); prod(k=1, #f~, if(2==f[k,1], (-1)^f[k, 2], -(1==f[k, 2]))); };
%o A359467(n) = ((A166486(n)+A355689(n))%2);
%Y Characteristic function of A359468, numbers that are either multiples of 4 with their odd part squarefree, or that are not multiples of 4 and not squarefree.
%Y Cf. A166486, A355689, A342419, A353627, A358839.
%Y Differs from A359466 for the first time at n=225, where a(225) = 1, while A359466(225) = 0.
%Y Differs from A359469 [= A353459(n) mod 2] for the first time at n=100. Here a(100) = 0.
%K nonn
%O 1
%A _Antti Karttunen_, Jan 02 2023
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