A107078 Whether n has non-unitary prime divisors.

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

Offset

1,1

Comments

Also the characteristic function of the numbers that are not squarefree: A013929. - Enrique Pérez Herrero, Jul 08 2012

The sequence of partial sums of this sequence is A057627. - Jason Kimberley, Feb 01 2017

Links

Enrique Pérez Herrero, Table of n, a(n) for n = 1..5000

Index entries for characteristic functions.

Formula

a(n) = 1 if A056170(n)>0, 0 otherwise.

a(n) = A107079(n) - A013928(n+1).

a(n) = 1 - A008966(n). - Reinhard Zumkeller, Oct 03 2008

a(n) = Sum_{k=0..n-1} (mu(n-k-1) mod 2) - Sum_{k=0..n-1} (mu(n-k) mod 2).

a(n) = abs(mu(n) - (-1)^omega(n)) = (mu(n) - (-1)^omega(n))^2 = abs(A008683(n) - (-1)^A001221(n)). - Enrique Pérez Herrero, Apr 28 2012

a(n) = 1 - mu(n)^2. - Enrique Pérez Herrero, Jul 08 2012

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 - 6/Pi^2 (A229099). - Amiram Eldar, Jul 24 2022

Maple

seq(1 - abs(numtheory:-mobius(n)), n = 1..101); # Peter Luschny, Jul 27 2023

Mathematica

Table[1-MoebiusMu[n]^2, {n, 1, 100}] (* Enrique Pérez Herrero, Jul 08 2012 *)

Prog

(Python)
from sympy import mobius
def A107078(n): return int(not mobius(n)) # Chai Wah Wu, Dec 05 2024

Crossrefs

Cf. A087049. - R. J. Mathar, Aug 24 2008

Cf. A013929, A008683, A008966, A107078, A229099.

Sequence in context: A359466 A359467 A359469 * A341613 A163533 A354982

Adjacent sequences: A107075 A107076 A107077 * A107079 A107080 A107081

Keyword

easy,nonn

Author

Paul Barry, May 10 2005

Status

approved