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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. 10
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]

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 *)

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

CROSSREFS

Cf. A035207, A046913, A054584.

Cf. A001227, A000005.

Sequence in context: A279027 A103151 A035221 * A297167 A303389 A276166

Adjacent sequences:  A035188 A035189 A035190 * A035192 A035193 A035194

KEYWORD

nonn,mult

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 19 18:51 EST 2019. Contains 320328 sequences. (Running on oeis4.)