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 A035191 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 9. 13
 1, 2, 1, 3, 2, 2, 2, 4, 1, 4, 2, 3, 2, 4, 2, 5, 2, 2, 2, 6, 2, 4, 2, 4, 3, 4, 1, 6, 2, 4, 2, 6, 2, 4, 4, 3, 2, 4, 2, 8, 2, 4, 2, 6, 2, 4, 2, 5, 3, 6, 2, 6, 2, 2, 4, 8, 2, 4, 2, 6, 2, 4, 2, 7, 4, 4, 2, 6, 2, 8, 2, 4, 2, 4, 3, 6, 4, 4, 2, 10, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Number of divisors of n not congruent to 0 mod 3. - Vladeta Jovovic, Oct 26 2001 a(n) is the number of factors (over Q) of the polynomial x^(2n) + x^n + 1 . a(n) = d(3n) - d(n) where d() is the divisor function. - Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 28 2003 Equals Mobius transform of A011655. - Gary W. Adamson, Apr 24 2009 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA Multiplicative with a(3^e)=1 and a(p^e)=e+1 for p<>3. G.f.: Sum_{k>0} x^k*(1+x^k)/(1-x^(3*k)). - Vladeta Jovovic, Dec 16 2002 a(n) = A001817(n) + A001822(n). [Reinhard Zumkeller, Nov 26 2011] a(n) = tau(3*n) - tau(n). - Ridouane Oudra, Sep 05 2020 MAPLE for n from 1 to 500 do a := ifactors(n):s := 1:for k from 1 to nops(a[2]) do p := a[2][k][1]:e := a[2][k][2]: if p=3 then b := 1:else b := e+1:fi:s := s*b:od:printf(`%d, `, s); od: # alternative A035191 := proc(n)     A001817(n)+A001822(n) ; end proc: [seq(A035191(n), n=1..100)] ; # R. J. Mathar, Sep 25 2017 MATHEMATICA a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[9, #] &]]; Table[ a[n], {n, 1, 100}] (* G. C. Greubel, Apr 27 2018 *) f[3, e_] := 1; f[p_, e_] := e+1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 26 2020 *) PROG (PARI) m=9; direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X)) (Haskell) a035191 n = a001817 n + a001822 n  -- Reinhard Zumkeller, Nov 26 2011 (MAGMA) [NumberOfDivisors(n)/Valuation(3*n, 3): n in [1..100]]; // Vincenzo Librandi, Jun 03 2019 CROSSREFS Cf. A035207, A046913, A054584. Cf. A001227, A000005. Sequence in context: A279027 A103151 A035221 * A297167 A325224 A303389 Adjacent sequences:  A035188 A035189 A035190 * A035192 A035193 A035194 KEYWORD nonn,mult,easy AUTHOR STATUS approved

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Last modified May 23 18:08 EDT 2022. Contains 353993 sequences. (Running on oeis4.)