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

4, 8, 9, 12, 16, 18, 20, 24, 25, 27, 28, 32, 40, 44, 45, 48, 49, 50, 52, 54, 56, 60, 63, 64, 68, 75, 76, 80, 81, 84, 88, 90, 92, 96, 98, 99, 104, 112, 116, 117, 120, 121, 124, 125, 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

Offset: 1

Author

Antti Karttunen, Jan 02 2023

Keywords

• nonn

Comments

Numbers k for which the sum A166486(k)+A353627(k) [equally: A166486(k)+A355689(k)] is odd.

The asymptotic density of this sequence is 3/4 - 4/Pi^2 = 0.344715... . - Amiram Eldar, Jan 24 2023

Examples

			8 is included because it is a multiple of 4, and A000265(8) = 1 is squarefree.
12 is included because it is a multiple of 4, and A000265(12) = 3 is squarefree.
225 = 3^2 * 5^2 is included because it is not a multiple of 4, and it is not squarefree.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000265, A166486, A355689, A359467 (characteristic function).

Positions of odd terms in A342419.

Differs from A190641 and A327877 for the first time at n=77, as a(77) = 225 is not included in them.

Programs

Mathematica

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 *)

PARI

isA359468(n) = A359467(n);