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A083040 Number of divisors of n that are <= 4 2
1, 2, 2, 3, 1, 3, 1, 3, 2, 2, 1, 4, 1, 2, 2, 3, 1, 3, 1, 3, 2, 2, 1, 4, 1, 2, 2, 3, 1, 3, 1, 3, 2, 2, 1, 4, 1, 2, 2, 3, 1, 3, 1, 3, 2, 2, 1, 4, 1, 2, 2, 3, 1, 3, 1, 3, 2, 2, 1, 4, 1, 2, 2, 3, 1, 3, 1, 3, 2, 2, 1, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Periodic of period 12. Parker vector of the wreath product of S_4 and S, the symmetric group of a countable set.

LINKS

Table of n, a(n) for n=1..72.

D. A. Gewurz and F. Merola, Sequences realized as Parker vectors of oligomorphic permutation groups, J. Integer Seq., 6 (2003), 03.1.6

Index entries for two-way infinite sequences

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

FORMULA

G.f.: x/(1-x)+x^2/(1-x^2)+x^3/(1-x^3)+x^4/(1-x^4).

a(n)=a(n-12)=a(-n).

a(n)=(1/792)*{223*(n mod 12)-173*[(n+1) mod 12]+91*[(n+2) mod 12]+25*[(n+3) mod 12]+91*[(n+4) mod 12]-107*[(n+5) mod 12]+157*[(n+6) mod 12]-107*[(n+7) mod 12]+157*[(n+8) mod 12]-41*[(n+9) mod 12]+25*[(n+10) mod 12]-41*[(n+11) mod 12]} with n>=0 - Paolo P. Lava, Nov 24 2006

a(n)=25/12 - (3/4)*( - 1)^n - 1/2*sin(Pi*n/2) - (1/3)*cos(2*Pi*n/3) - (1/3)*3^(1/2)*sin(2*Pi*n/3) [From 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) + sum(k=1..4, cos(n*(k - 1)/4*2*Pi)/4). - Mats Granvik, Sep 09 2012

CROSSREFS

Cf. A083039, A000005

Sequence in context: A166248 A180257 A265576 * A083899 A190263 A144911

Adjacent sequences:  A083037 A083038 A083039 * A083041 A083042 A083043

KEYWORD

easy,nonn

AUTHOR

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

STATUS

approved

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Last modified June 1 19:32 EDT 2020. Contains 334762 sequences. (Running on oeis4.)