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

1,1

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

Links

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

Example

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.

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 *)

Prog

(PARI) isA359468(n) = A359467(n);

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.

Sequence in context: A359470 A190641 A327877 * A034043 A278517 A053443

Adjacent sequences: A359465 A359466 A359467 * A359469 A359470 A359471

Keyword

nonn

Author

Antti Karttunen, Jan 02 2023

Status

approved