login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A066829 1 if product of odd number of primes; 0 if product of even number of primes. 20
0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(A026424(n)) = 1; a(A028260(n)) = 0.

Contribution from Reinhard Zumkeller, Jul 01 2009: (Start)

The first N Terms are constructed by the following sieving process:

for j:=1 until N do a(j):=0,

for i:=1 until N/2 do

for j:=2*i step i until N do a(j):=1-a(i). (End)

REFERENCES

Cf. A065043.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

S. Ramanujan, Irregular numbers, J. Indian Math. Soc., 5 (1913), 105-106; Coll. Papers 20-21 (provides Dirichlet g.f.)

Index entries for characteristic functions

Index entries for sequences generated by sieves [From Reinhard Zumkeller, Jul 01 2009]

FORMULA

a(n) = (A008836(n) - 1) / 2.

a(m*n) = a(m) XOR a(n). [Reinhard Zumkeller, Aug 28 2008]

a(n) = A001222(n) mod 2. [Reinhard Zumkeller, Nov 19 2011]

EXAMPLE

Contribution from Reinhard Zumkeller, Jul 01 2009: (Start)

Sieve for N = 30, also demonstrating the affinity to the Sieve of Eratosthenes:

[initial] a(j):=0, 1<=j<=30:

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

[i=1] a(1)=0 --> a(j):=1, 2<=j<=30:

0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

[i=2] a(2)=1 --> a(2*j):=0, 2<=j<=[30/2]:

0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0

[i=3] a(3)=1 --> a(3*j):=0, 2<=j<=[30/3]:

0 1 1 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

[i=4] a(4)=0 --> a(4*j):=1, 2<=j<=[30/4]:

0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 0 0 1 1 0

[i=5] a(5)=1 --> a(5*j):=0, 2<=j<=[30/5]:

0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0

[i=6] a(6)=0 --> a(6*j):=1, 2<=j<=[30/6]:

0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 1 1 1 1 0 0 0 1 1 0 0 0 1 1 1

[i=7] a(7)=1 --> a(7*j):=0, 2<=j<=[30/7]:

0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1

[i=8] a(8)=1 --> a(8*j):=0, 2<=j<=[30/8]:

0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 1 1

[i=9] a(9)=0 --> a(9*j):=1, 2<=j<=[30/9]:

0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 1 1

[i=10] a(10)=0 --> a(10*j):=1, 2<=j<=[30/10]:

0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 1 1 1 0 0 1 0 0 0 1 0 1 1

and so on: a(22):=0 in [i=11], a(24):=0 in [i=12], a(26):=0 in [i=13], a(28):=1 in [i=14], and a(30):=1 in [i=15]. (End)

MAPLE

A066829 := proc(n)

    modp(numtheory[bigomega](n) , 2) ;

end proc:

seq(A066829(n), n=1..80) ; # R. J. Mathar, Jul 15 2017

MATHEMATICA

Table[(1-LiouvilleLambda[n])/2, {n, 1, 20}] (* Enrique Pérez Herrero, Jul 07 2012 *)

Table[If[OddQ[PrimeOmega[n]], 1, 0], {n, 120}] (* Harvey P. Dale, Mar 12 2016 *)

PROG

(PARI) A066829(n)=if(bigomega(n)%2==1, 1, 0)

(Haskell)

a066829 = (`mod` 2) . a001222 -- Reinhard Zumkeller, Nov 19 2011

CROSSREFS

Cf. A065043.

Cf. A072203, A055038 (partial sums), A001222.

Sequence in context: A189687 A284653 A099104 * A194664 A285975 A213729

Adjacent sequences:  A066826 A066827 A066828 * A066830 A066831 A066832

KEYWORD

nonn,easy

AUTHOR

G. L. Honaker, Jr., Jan 17 2002

EXTENSIONS

Corrected and comment added by Reinhard Zumkeller, Jun 26 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 13 18:57 EDT 2019. Contains 327981 sequences. (Running on oeis4.)