A353629 a(n) = 1 if n is a product of an even number of distinct primes, otherwise 0.

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

Offset

1

Links

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

Index entries for characteristic functions.

Index entries for sequences computed from exponents in factorization of n.

Formula

a(n) = 1 iff A008683(n) = +1 (if the Möbius mu-function obtains a positive value), otherwise 0.

a(n) = A008966(n) * A065043(n).

a(n) = A008966(n) - A252233(n).

a(n) = a(A046523(n)).

a(n) >= A280710(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 3/Pi^2 (A104141). - Amiram Eldar, Jul 24 2022

Mathematica

a[n_] := If[MoebiusMu[n] == 1, 1, 0]; Array[a, 100] (* Amiram Eldar, Jul 24 2022 *)

Prog

(PARI) A353629(n) = (1==moebius(n));

Crossrefs

Characteristic function of A030229.

Cf. A008683, A008966, A065043, A104141, A252233, A280710.

After n=1 differs for the next time from A280710 at n=210, where a(210) = 1, while A280710(210) = 0.

Sequence in context: A014359 A079998 A356170 * A339661 A320656 A354819

Adjacent sequences: A353626 A353627 A353628 * A353630 A353631 A353632

Keyword

nonn

Author

Antti Karttunen, May 02 2022

Status

approved