A373154 a(n) = 1 if 6*n is squarefree, otherwise 0.

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

Multiplicative with a(p^e) = 0 if p <= 3 or e >= 2, and 1 otherwise.

a(n) = A008966(A008588(n)) = A008966(n) * A354354(n).

a(n) = abs(A355688(n)) = A355688(n) mod 2.

From Amiram Eldar, May 29 2024: (Start)

Dirichlet g.f.: (2^s/(2^s+1)) * (3^s/(3^s+1)) * zeta(s)/zeta(2*s).

Sum_{k=1..n} a(k) ~ (3/Pi^2) * n. (End)

Mathematica

a[n_] := If[SquareFreeQ[6*n], 1, 0]; Array[a, 100] (* Amiram Eldar, May 29 2024 *)

Prog

(PARI) A373154(n) = issquarefree(6*n);
(PARI) A373154(n) = { my(f = factor(n)); prod(k=1, #f~, f[k, 2] < (2-(f[k, 1]<=3))); };

Crossrefs

Characteristic function of A276378.

Absolute values and also parity of A355688.

Cf. A008588, A008966, A354354.

Sequence in context: A267056 A089024 A355688 * A353488 A232991 A168553

Adjacent sequences: A373151 A373152 A373153 * A373155 A373156 A373157

Keyword

nonn,easy,mult

Author

Antti Karttunen, May 28 2024

Status

approved