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%I #11 Jun 23 2018 14:49:57
%S 1,-1,-1,2,-1,1,-1,-3,2,1,-1,-2,-1,1,1,4,-1,-2,-1,-2,1,1,-1,3,2,1,-3,
%T -2,-1,-1,-1,-5,1,1,1,4,-1,1,1,3,-1,-1,-1,-2,-2,1,-1,-4,2,-2,1,-2,-1,
%U 3,1,3,1,1,-1,2,-1,1,-2,6,1,-1,-1,-2,1,-1,-1,-6,-1,1,-2,-2,1,-1,-1,-4,4,1,-1
%N a(n) = lambda(n)*E(n), where lambda(n) = A008836(n) and E(n) = A005361(n).
%F Multiplicative with a(p^e) = e*(-1)^e, p prime and e > 0.
%F Dirichlet g.f.: (zeta(2*s))^2 / (zeta(s)*zeta(3*s)).
%F Dirichlet convolution with A048691(n) yields A092520(n).
%F Dirichlet inverse b(n), n>=1, is multiplicative with b(1)=1 and for p prime and e>0: b(p^e) = 0 if e mod 3 = 0 otherwise b(p^e) = (-1)^(3 - e mod 3).
%t Array[LiouvilleLambda[#] Apply[Times, FactorInteger[#][[All, -1]] ] &, 83] (* _Michael De Vlieger_, May 06 2018 *)
%o (PARI) a(n) = (-1)^bigomega(n)*factorback(factor(n)[, 2]); \\ _Michel Marcus_, May 05 2018
%Y Signed version of A005361.
%Y Cf. A008836, A048691, A092520.
%K sign,easy,mult
%O 1,4
%A _Werner Schulte_, May 02 2018
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