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A219009 Coefficients of the Dirichlet series for zeta(4s)/zeta(s). 5
1, -1, -1, 0, -1, 1, -1, 0, 0, 1, -1, 0, -1, 1, 1, 1, -1, 0, -1, 0, 1, 1, -1, 0, 0, 1, 0, 0, -1, -1, -1, -1, 1, 1, 1, 0, -1, 1, 1, 0, -1, -1, -1, 0, 0, 1, -1, -1, 0, 0, 1, 0, -1, 0, 1, 0, 1, 1, -1, 0, -1, 1, 0, 0, 1, -1, -1, 0, 1, -1, -1, 0, -1, 1, 0, 0, 1, -1, -1, -1, 1, 1, -1, 0, 1, 1, 1, 0, -1, 0, 1, 0, 1, 1, 1, 1, -1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

Different from A197774.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from exponents in factorization of n

FORMULA

G.f.: Sum_{n>=1} a(n)*x^n/(1 - x^n)  =  Sum_{n>=1} x^(n^4). - Geoffrey Critzer, Mar 20 2015

MAPLE

Z := proc(n, k)

    local a, pf, e ;

    a := 1 ;

    for pf in ifactors(n)[2] do

        e := pf[2] ;

        if modp(e, k) = 0 then

            ;

        elif modp(e, k) = 1 then

            a := -a ;

        else

            a := 0 ;

        end if;

    end do;

    a;

end proc:

A219009 := proc(n)

    Z(n, 4) ;

end proc: # R. J. Mathar, May 28 2016

MATHEMATICA

nn = 100; f[x_] := Sum[a[n] x^n/(1 - x^n), {n, 1, nn}]; sol = SolveAlways[0 == Series[f[x] - Sum[x^(n^4), {n, 1, nn}], {x, 0, nn}], x]; Table[a[n], {n, 1, nn}] /. sol // Flatten (* Geoffrey Critzer, Mar 20 2015 *)

PROG

(PARI) a(n)=sumdiv(n, d, if(issquare(d), issquare(sqrtint(d)), 0)*moebius(n/d))

(PARI) for(n=1, 100, print1(direuler(p=2, n, (1-X)/(1-X^4))[n], ", ")) \\ Vaclav Kotesovec, Jun 14 2020

CROSSREFS

Cf. A008836, A210826, A253206, A307430 (Dirichlet inverse).

Differs from A197774 for the first time at n=32, where a(32) = -1, while A197774(32) = 0.

Sequence in context: A323154 A060038 A197774 * A267708 A167021 A267687

Adjacent sequences:  A219006 A219007 A219008 * A219010 A219011 A219012

KEYWORD

sign,mult

AUTHOR

Benoit Cloitre, Nov 09 2012

STATUS

approved

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Last modified July 15 00:05 EDT 2020. Contains 335762 sequences. (Running on oeis4.)