A353675 a(n) = 1 if n is an odd number with an even number of distinct prime factors, otherwise 0.

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions

Formula

a(n) = A000035(n) * (1-A092248(n)).

a(n) = A000035(n) - A353673(n).

a(n) >= A353676(n).

Example

n = 45 = 3^2 * 5 is an odd number with two distinct prime factors, therefore a(45) = 1.
n = 1155 = 3*5*7*11 is an odd number with four distinct prime factors, therefore a(1155) = 1.

Mathematica

Table[If[OddQ[n]&&EvenQ[PrimeNu[n]], 1, 0], {n, 130}] (* Harvey P. Dale, Feb 07 2024 *)

Prog

(PARI) A353675(n) = ((n%2) && !(omega(n)%2));

Crossrefs

Characteristic function of {1} UNION A098905.

Cf. A000035, A001221, A092248, A353672, A353673, A353674.

After n=1 differs from A353676 for the next time at n=1155, where a(1155)=1, while A353676(1155)=0.

Cf. also A353557.

Sequence in context: A014041 A373258 A359465 * A373137 A015868 A323402

Adjacent sequences: A353672 A353673 A353674 * A353676 A353677 A353678

Keyword

nonn

Author

Antti Karttunen, May 03 2022

Status

approved