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A092248 Parity of number of distinct primes dividing n (function omega(n)) parity of A001221. 9
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 (list; graph; refs; listen; history; text; internal format)
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: A189727 A268411 A069513 * A106743 A284944 A284674

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

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Last modified February 17 18:14 EST 2020. Contains 332005 sequences. (Running on oeis4.)