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A001817 G.f.: Sum_{n>0} x^n/(1-x^(3n)) = Sum_{n>=0} x^(3n+1)/(1-x^(3n+1)). 13
1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 2, 2, 2, 1, 4, 1, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 4, 1, 2, 2, 3, 1, 2, 1, 3, 3, 3, 1, 4, 1, 1, 2, 4, 2, 2, 1, 3, 2, 2, 2, 4, 2, 2, 2, 3, 1, 4, 1, 2, 2, 2, 2, 4, 2, 2, 2, 5, 1, 2, 1, 4, 2, 2, 1, 4, 1, 2, 4, 3, 2, 2, 2, 3, 2, 3, 1, 5, 1, 2, 2, 4, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(n) is the number of positive divisors of n of the form 3k+1. If r(n) denotes the number of representations of n by the quadratic form j^2+ij+i^2, then r(n)= 6 *(a(n)-A001822(n)). - Benoit Cloitre, Jun 24 2002

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 infinitésimale à la théorie des nombres, J. Reine Angew. Math. 21 (1840), 1-12.

Michael Gilleland, Some Self-Similar Integer Sequences

FORMULA

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

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

Equals A051731 * [1, 0, 0, 1, 0, 0, 1, 0, 0, 1, ...]. - Gary W. Adamson, Nov 06 2007

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

EXAMPLE

x + x^2 + x^3 + 2*x^4 + x^5 + x^6 + 2*x^7 + 2*x^8 + x^9 + ...

MAPLE

A001817 := proc(n)

    local a, d ;

    a := 0 ;

    for d in numtheory[divisors](n) do

        if modp(d, 3) = 1 then

            a := a+1 ;

        end if ;

    end do:

    a ;

end proc:

seq(A001817(n), n=1..100) ; # R. J. Mathar, Sep 25 2017

MATHEMATICA

a[n_] := DivisorSum[n, Boole[Mod[#, 3] == 1]&]; Array[a, 100] (* Jean-François Alcover, Dec 01 2015 *)

PROG

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

(Haskell)

a001817 n = length [d | d <- [1, 4..n], mod n d == 0]

-- Reinhard Zumkeller, Nov 26 2011

CROSSREFS

Cf. A001822, A035191, A002324.

Cf. A051731.

Sequence in context: A305830 A093914 A007061 * A214973 A091954 A325167

Adjacent sequences:  A001814 A001815 A001816 * A001818 A001819 A001820

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified April 16 07:59 EDT 2021. Contains 343030 sequences. (Running on oeis4.)