The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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