A083040 Number of divisors of n that are <= 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, 1, 2, 2, 3, 1, 3, 1, 3, 2, 2, 1, 4

Offset: 1

Author

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

Keywords

• easy
• nonn

Comments

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

Links

• 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).

Crossrefs

Cf. A083039, A000005

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) = 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