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A359468 Numbers that are either multiples of 4 with their odd part squarefree, or that are not multiples of 4 and not squarefree.

%I A359468 #18 Jan 24 2023 02:50:55
%S A359468 4,8,9,12,16,18,20,24,25,27,28,32,40,44,45,48,49,50,52,54,56,60,63,64,
%T A359468 68,75,76,80,81,84,88,90,92,96,98,99,104,112,116,117,120,121,124,125,
%U A359468 126,128,132,135,136,140,147,148,150,152,153,156,160,162,164,168,169,171,172,175,176,184,188,189,192,198,204,207,208,212,220,224,225,228
%N A359468 Numbers that are either multiples of 4 with their odd part squarefree, or that are not multiples of 4 and not squarefree.
%C A359468 Numbers k for which the sum A166486(k)+A353627(k) [equally: A166486(k)+A355689(k)] is odd.
%C A359468 The asymptotic density of this sequence is 3/4 - 4/Pi^2 = 0.344715... . - _Amiram Eldar_, Jan 24 2023
%H A359468 Amiram Eldar, <a href="/A359468/b359468.txt">Table of n, a(n) for n = 1..10000</a>
%e A359468 8 is included because it is a multiple of 4, and A000265(8) = 1 is squarefree.
%e A359468 12 is included because it is a multiple of 4, and A000265(12) = 3 is squarefree.
%e A359468 225 = 3^2 * 5^2 is included because it is not a multiple of 4, and it is not squarefree.
%t A359468 q[n_] := Module[{e = IntegerExponent[n, 2], o}, o = n/2^e; sqf = SquareFreeQ[o]; (e > 1 && sqf) || (e < 2 && ! sqf)]; Select[Range[250], q] (* _Amiram Eldar_, Jan 24 2023 *)
%o A359468 (PARI) isA359468(n) = A359467(n);
%Y A359468 Cf. A000265, A166486, A355689, A359467 (characteristic function).
%Y A359468 Positions of odd terms in A342419.
%Y A359468 Differs from A190641 and A327877 for the first time at n=77, as a(77) = 225 is not included in them.
%K A359468 nonn
%O A359468 1,1
%A A359468 _Antti Karttunen_, Jan 02 2023