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

%I A083039 #63 Jul 19 2024 13:28:34
%S A083039 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 A083039 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 A083039 2,2,1,3,1,2,2,2,1,3,1,2,2,2,1,3,1,2,2,2,1,3
%N A083039 Number of divisors of n that are <= 3.
%C A083039 Periodic of period 6. Parker vector of the wreath product of S_3 and S, the symmetric group of a countable set.
%H A083039 Antti Karttunen, <a href="/A083039/b083039.txt">Table of n, a(n) for n = 1..12000</a>
%H A083039 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 A083039 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 A083039 <a href="/index/Tu#2wis">Index entries for two-way infinite sequences</a>
%H A083039 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-1, 0, 1, 1).
%F A083039 G.f.: x/(1-x) + x^2/(1-x^2) + x^3/(1-x^3).
%F A083039 a(n) = a(n-6) = a(-n).
%F A083039 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 A083039 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 A083039 a(n) = log_2(gcd(n,2) + gcd(n,6)). - _Gary Detlefs_, Feb 15 2014
%F A083039 a(n) = Sum_{d|n, d<=3} 1. - _Wesley Ivan Hurt_, Oct 30 2023
%e A083039 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 A083039 LinearRecurrence[{-1, 0, 1, 1},{1, 2, 2, 2},90] (* _Ray Chandler_, Aug 26 2015 *)
%o A083039 (PARI) a(n)=[3,1,2,2,2,1][n%6+1];
%Y A083039 Cf. A000005, A007310, A008588, A047228, A083040, A138553.
%K A083039 easy,nonn
%O A083039 1,2
%A A083039 Daniele A. Gewurz (gewurz(AT)mat.uniroma1.it) and Francesca Merola (merola(AT)mat.uniroma1.it), May 06 2003