A359158 a(n) = 1 if the odd part of n is squarefree and the number of prime factors of n (with multiplicity) is odd, otherwise 0.

0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0

Offset

1

Comments

a(n) = 1 if A000265(n) is squarefree and A001222(n) is odd, otherwise 0.

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions.

Formula

a(n) = A066829(n) * A353627(n).

a(n) = A353627(n) - A359156(n).

a(n) = [A355689(n) < 0], where [ ] is the Iverson bracket.

a(n) >= A010051(n).

Sum_{k=1..n} a(k) ~ (4/Pi^2)*n. - Amiram Eldar, Jan 18 2023

Mathematica

a[n_] := If[OddQ[PrimeOmega[n]] && SquareFreeQ[n/2^IntegerExponent[n, 2]], 1, 0]; Array[a, 100] (* Amiram Eldar, Jan 18 2023 *)

Prog

(PARI) A359158(n) = ((bigomega(n)%2)&&issquarefree(n>>valuation(n, 2)));

Crossrefs

Characteristic function of A359159.

Cf. A000265, A001222, A010051, A066829, A166486, A185199, A353627, A355689, A359156.

Sequence in context: A189687 A353817 A284653 * A099104 A358769 A066829

Adjacent sequences: A359155 A359156 A359157 * A359159 A359160 A359161

Keyword

nonn

Author

Antti Karttunen, Dec 20 2022

Status

approved