A092248 Parity of number of distinct primes dividing n (function omega(n)) parity of A001221.

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

Offset

1,1

Comments

a(p^r) = 1 for all primes p and all exponents r>0. - Tom Edgar, Mar 22 2015

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Index entries for characteristic functions

Formula

If omega(n) is even then a(n) = 0 else a(n) = 1. By convention, a(1) = 0. (Also because A001221(1) = 0 is an even number too).

a(n) = A000035(A001221(n)). - Michel Marcus, Mar 22 2015

a(n) = A268411(A156552(n)). - Antti Karttunen, May 30 2017

Example

For n = 1, 0 primes divide 1 so a(1)=0.
For n = 2, there is 1 distinct prime dividing 2 (itself) so a(2)=1.
For n = 4 = 2^2, there is 1 distinct prime dividing 4 so a(4)=1.
For n = 5, there is 1 distinct prime dividing 5 (itself) so a(5)=1.
For n = 6 = 2*3, there are 2 distinct primes dividing 6 so a(6)=0.

Mathematica

Table[Boole[OddQ[PrimeNu[n]]], {n, 1, 100}] (* Geoffrey Critzer, Feb 16 2015 *)

Prog

(PARI) for (i=1, 200, if(Mod(omega(i), 2)==0, print1(0, ", "), print1(1, ", ")))
(Python)
from sympy import primefactors
def a(n): return 0 if n==1 else 1*(len(primefactors(n))%2==1) # Indranil Ghosh, Jun 01 2017

Crossrefs

Cf. A001221, A268411.

Sequence in context: A361113 A268411 A069513 * A354920 A106743 A284944

Adjacent sequences: A092245 A092246 A092247 * A092249 A092250 A092251

Keyword

easy,nonn

Author

Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Feb 19 2004

Extensions

Offset corrected by Reinhard Zumkeller, Oct 03 2008

Status

approved