1,1

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

Contribution from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 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)

Index entries for characteristic functions

Index entries for sequences generated by sieves [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 01 2009]

a(m*n) = a(m) XOR a(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 28 2008]

Contribution from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 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)

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

Cf. A065043.

Sequence in context: A139689 A073070 A099104 this_sequence A048820 A144101 A127000

Adjacent sequences: A066826 A066827 A066828 this_sequence A066830 A066831 A066832

nonn

G. L. Honaker, Jr. (honak3r(AT)gmail.com), Jan 17 2002

More terms from Jason Earls (zevi_35711(AT)yahoo.com), Jan 21 2002

Corrected and comment added by Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 26 2009