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A083039
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Number of divisors of n that are <= 3.
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8
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1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3
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OFFSET
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1,2
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COMMENTS
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Periodic of period 6. Parker vector of the wreath product of S_3 and S, the symmetric group of a countable set.
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LINKS
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FORMULA
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G.f.: x/(1-x) + x^2/(1-x^2) + x^3/(1-x^3).
a(n) = a(n-6) = a(-n).
a(n) = 11/6 - (1/2)*(-1)^n - (1/3)*cos(2*Pi*n/3) - (1/3)*3^(1/2)*sin(2*Pi*n/3). - Richard Choulet, Dec 12 2008
a(n) = Sum_{k=1..1} cos(n*(k - 1)/1*2*Pi)/1 + Sum_{k=1..2} cos(n*(k - 1)/2*2*Pi)/2 + Sum_{k=1..3} cos(n*(k - 1)/3*2*Pi)/3. - Mats Granvik, Sep 09 2012
a(n) = log_2(gcd(n,2) + gcd(n,6)). - Gary Detlefs, Feb 15 2014
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EXAMPLE
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The divisors of 6 are 1, 2, 3 and 6. Of those divisors, 1, 2 and 3 are <= 3. That's three divisors, therefore, a(6) = 3. - David A. Corneth, Sep 30 2017
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MATHEMATICA
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LinearRecurrence[{-1, 0, 1, 1}, {1, 2, 2, 2}, 90] (* Ray Chandler, Aug 26 2015 *)
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PROG
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(PARI) a(n)=[3, 1, 2, 2, 2, 1][n%6+1];
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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Daniele A. Gewurz (gewurz(AT)mat.uniroma1.it) and Francesca Merola (merola(AT)mat.uniroma1.it), May 06 2003
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STATUS
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approved
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