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A083039 Number of divisors of n that are <= 3. 5

%I

%S 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,

%T 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,

%U 2,2,1,3,1,2,2,2,1,3,1,2,2,2,1,3,1,2,2,2,1,3

%N Number of divisors of n that are <= 3.

%C Periodic of period 6. Parker vector of the wreath product of S_3 and S, the symmetric group of a countable set.

%C Terms of the simple continued fraction of 4/(sqrt(78)-6). Decimal expansion of 1343/10989. - _Paolo P. Lava_, Aug 05 2009

%H D. A. Gewurz and F. Merola, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL6/Gewurz/gewurz5.html">Sequences realized as Parker vectors of oligomorphic permutation groups</a>, J. Integer Seq., 6 (2003), 03.1.6

%H M. D. Hirschhorn, J. A. Sellers, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL11/Sellers/sellers44.html">Enumeration of unigraphical partitions</a>, JIS 11 (2008) 08.4.6

%H <a href="/index/Tu#2wis">Index entries for two-way infinite sequences</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-1, 0, 1, 1).

%F G.f.: x/(1-x) + x^2/(1-x^2) + x^3/(1-x^3).

%F a(n) = a(n-6) = a(-n).

%F a(n) = (1/90)*(41*(n mod 6) - 19*((n+1) mod 6) + 26*((n+2) mod 6) + 11*((n+3) mod 6) + 11*((n+4) mod 6) - 4*((n+5) mod 6)) with n >= 0. - _Paolo P. Lava_, Nov 27 2006

%F 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

%F 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

%F a(n) = log_2(gcd(n,2) + gcd(n,6)). - _Gary Detlefs_, Feb 15 2014

%e 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

%t LinearRecurrence[{-1, 0, 1, 1},{1, 2, 2, 2},90] (* _Ray Chandler_, Aug 26 2015 *)

%o (PARI) a(n)=[3,1,2,2,2,1][n%6+1];

%Y Cf. A000005, A007310, A008588, A047228, A083040, A138553.

%K easy,nonn

%O 1,2

%A Daniele A. Gewurz (gewurz(AT)mat.uniroma1.it) and Francesca Merola (merola(AT)mat.uniroma1.it), May 06 2003

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Last modified April 12 17:48 EDT 2021. Contains 342929 sequences. (Running on oeis4.)