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A001822 Expansion of Sum x^(3n+2)/(1-x^(3n+2)), n=0..inf. 12
0, 1, 0, 1, 1, 1, 0, 2, 0, 2, 1, 1, 0, 2, 1, 2, 1, 1, 0, 3, 0, 2, 1, 2, 1, 2, 0, 2, 1, 2, 0, 3, 1, 2, 2, 1, 0, 2, 0, 4, 1, 2, 0, 3, 1, 2, 1, 2, 0, 3, 1, 2, 1, 1, 2, 4, 0, 2, 1, 3, 0, 2, 0, 3, 2, 2, 0, 3, 1, 4, 1, 2, 0, 2, 1, 2, 2, 2, 0, 5, 0, 2, 1, 2, 2, 2, 1, 4, 1, 2, 0, 3, 0, 2, 2, 3, 0, 3, 1, 4, 1, 2, 0, 4, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

a(n) is the number of positive divisors of n of the form 3k+2. If r(n) denotes the number of representations of n by the quadratic form j^2+i*j+i^2, then r(n)= 6 *(A001817(n)-a(n)). - Benoit Cloitre, Jun 24 2002

a(n) = (A035191(n) - A002324(n)) / 2. - Reinhard Zumkeller, Nov 26 2011

REFERENCES

B. C. Berndt,"On a certain theta-function in a letter of Ramanujan from Fitzroy House", Ganita 43 (1992),33-43.

LINKS

Nick Hobson, Table of n, a(n) for n = 1..10000

P. G. Dirichlet, Recherches sur diverses applications de l'analyse infinitesimale a la theorie des nombres, J. Reine Angew. Math. 21 (1840), 1-12.

Michael Gilleland, Some Self-Similar Integer Sequences

FORMULA

Moebius transform is period 3 sequence [0, 1, 0, ...]. - Michael Somos, Sep 20 2005

G.f.: Sum_{k>0} x^(3k-1)/(1-x^(3k-1)) = Sum_{k>0} x^(2k)/(1-x^(3k)). - Michael Somos, Sep 20 2005

a(n) + A001817(n) + A000005(n/3) = A000005(n), where A000005(.)=0 if the argument is not an integer. - R. J. Mathar, Sep 25 2017

MAPLE

A001822 := proc(n)

    local a, d ;

    a := 0 ;

    for d in numtheory[divisors](n) do

        if modp(d, 3) = 2 then

            a := a+1 ;

        end if ;

    end do:

    a ;

end proc:

seq(A001822(n), n=1..100) ; # R. J. Mathar, Sep 25 2017

MATHEMATICA

a[n_] := DivisorSum[n, Boole[Mod[#, 3] == 2]&]; Array[a, 100] (* Jean-Fran├žois Alcover, Dec 01 2015 *)

PROG

(PARI) a(n)=if(n<1, 0, sumdiv(n, d, d%3==2))

(Haskell)

a001822 n = length [d | d <- [2, 5..n], mod n d == 0]

-- Reinhard Zumkeller, Nov 26 2011

CROSSREFS

Cf. A001817.

Sequence in context: A287263 A102442 A091182 * A249603 A231714 A339893

Adjacent sequences:  A001819 A001820 A001821 * A001823 A001824 A001825

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified April 16 05:26 EDT 2021. Contains 343030 sequences. (Running on oeis4.)