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A299406 G.f.: Sum_{n>0} a(n)/n^s = ((zeta(s)*zeta(6*s))/((zeta(2*s)*zeta(3*s)). 3
1, 1, 1, 0, 1, 1, 1, -1, 0, 1, 1, 0, 1, 1, 1, -1, 1, 0, 1, 0, 1, 1, 1, -1, 0, 1, -1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, -1, 1, 1, 1, 0, 0, 1, 1, -1, 0, 0, 1, 0, 1, -1, 1, -1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, -1, -1, 1, 1, 0, 1, 1, 1, -1, 1, 0, 1, 0, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

Vaclav Kotesovec, Plot of Sum_{k=1..n} a(k) / (2*n*Pi^4/(315*Zeta(3))) for n = 1..1000000

Index entries for sequences computed from exponents in factorization of n

FORMULA

a(n) is multiplicative with a(p^e)=(-1)^(e mod 3 + e mod 6) if e mod 3 < 2, otherwise 0, p prime and e >= 0.

Dirichlet inverse b(n) is multiplicative with b(p^e) = (-1)^e if e < 3, otherwise 0, p prime and e >= 0.

Sum_{d|n} a(d)*A005361(n/d) = A000005(n).

Conjecture: a(n) = A008836(n) * A210826(n).

Sum_{k=1..n} a(k) ~ 2*n*Pi^4/(315*Zeta(3)). - Vaclav Kotesovec, Feb 08 2019

MATHEMATICA

f[e_] := If[Mod[e, 3] < 2, (-1)^(Mod[e, 3] + Mod[e, 6]), 0];

a[n_] := a[n] = Times @@ (f /@ FactorInteger[n][[All, 2]]);

Array[a, 100] (* Jean-Fran├žois Alcover, Feb 26 2018 *)

PROG

(PARI) A299406(n) = { my(es = factor(n)[, 2]); factorback(apply(e -> if(2==(e%3), 0, (-1)^((e%3)+(e%6))), es)); }; \\ Antti Karttunen, Jul 29 2018

CROSSREFS

Cf. A000005, A005361, A008836, A210826.

Sequence in context: A307425 A210826 A307421 * A287769 A267866 A175087

Adjacent sequences:  A299403 A299404 A299405 * A299407 A299408 A299409

KEYWORD

sign,mult

AUTHOR

Werner Schulte, Feb 20 2018

STATUS

approved

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Last modified November 21 00:12 EST 2019. Contains 329348 sequences. (Running on oeis4.)