A359465 a(n) = 1 if n is an odd squarefree number with an even number of 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, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0

Offset

1

Links

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

Index entries for characteristic functions.

Formula

a(n) = A000035(n) * A353629(n).

a(n) = A008966(n) * A353557(n) = A008966(n) * A353675(n).

a(n) = A065043(n) * A323239(n) = A323239(n) * A359464(n).

a(n) = [A343370(n) = 1], where [ ] is the Iverson bracket.

For all n >= 1, a(n) >= A353481(n).

Sum_{k=1..n} a(k) ~ c * n, where c = 2/Pi^2 (A185197). - Amiram Eldar, Jan 05 2023

Mathematica

a[n_] := If[OddQ[n] && MoebiusMu[n] == 1, 1, 0]; Array[a, 100] (* Amiram Eldar, Jan 05 2023 *)

Prog

(PARI)
A065043(n) = (1 - (bigomega(n)%2));
A323239(n) = ((n%2) && issquarefree(n));
A359465(n) = (A323239(n)&&A065043(n));

Crossrefs

Characteristic function of A056913.

Cf. A000035, A008966, A065043, A185197, A323239, A343370, A353557, A353629, A353675, A359464.

After n=1 differs from A353481 for the next time at n=1155, where a(1155)=1, while A353481(1155)=0. Cf. also A046390.

Sequence in context: A358008 A249832 A014041 * A353675 A015868 A323402

Adjacent sequences: A359462 A359463 A359464 * A359466 A359467 A359468

Keyword

nonn

Author

Antti Karttunen, Jan 02 2023

Status

approved