A359156 a(n) = 1 if the odd part of n is squarefree and the number of prime factors of n (with multiplicity) is even, otherwise 0.

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

Offset

1

Comments

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

Links

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

Index entries for characteristic functions.

Formula

a(n) = A065043(n) * A353627(n).

a(n) = A353627(n) - A359158(n).

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

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

Mathematica

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

Prog

(PARI) A359156(n) = ((0==(bigomega(n)%2))&&issquarefree(n>>valuation(n, 2)));

Crossrefs

Characteristic function of A359157.

Cf. A000265, A001222, A065043, A166486, A185199, A353627, A355689, A359158.

Sequence in context: A214264 A173858 A217586 * A352569 A101266 A260552

Adjacent sequences: A359153 A359154 A359155 * A359157 A359158 A359159

Keyword

nonn

Author

Antti Karttunen, Dec 20 2022

Status

approved