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A066829
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1 if product of odd number of primes; 0 if product of even number of primes.
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8
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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; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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)
a(n) = (A008836(n) + 1) / 2.
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for characteristic functions
Index entries for sequences generated by sieves [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 01 2009]
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FORMULA
| a(m*n) = a(m) XOR a(n). [Reinhard Zumkeller, Aug 28 2008]
a(n) = A001222(n) mod 2. [Reinhard Zumkeller, Nov 19 2011]
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EXAMPLE
| 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)
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PROG
| (PARI) A066829(n)=if(bigomega(n)%2==1, 1, 0)
(Haskell)
a066829 = (`mod` 2) . a001222 -- Reinhard Zumkeller, Nov 19 2011
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CROSSREFS
| Cf. A065043.
Cf. A072203, A055038 (partial sums), A001222.
Sequence in context: A139689 A073070 A099104 * A174207 A048820 A144101
Adjacent sequences: A066826 A066827 A066828 * A066830 A066831 A066832
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KEYWORD
| nonn
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AUTHOR
| G. L. Honaker, Jr. (honak3r(AT)gmail.com), Jan 17 2002
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EXTENSIONS
| 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
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