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A303915 a(n) = lambda(n)*E(n), where lambda(n) = A008836(n) and E(n) = A005361(n). 0
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, -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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..83.

FORMULA

Multiplicative with a(p^e) = e*(-1)^e, p prime and e > 0.

Dirichlet g.f.: (zeta(2*s))^2 / (zeta(s)*zeta(3*s)).

Dirichlet convolution with A048691(n) yields A092520(n).

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).

MATHEMATICA

Array[LiouvilleLambda[#] Apply[Times, FactorInteger[#][[All, -1]] ] &, 83] (* Michael De Vlieger, May 06 2018 *)

PROG

(PARI) a(n) = (-1)^bigomega(n)*factorback(factor(n)[, 2]); \\ Michel Marcus, May 05 2018

CROSSREFS

Signed version of A005361.

Cf. A008836, A048691, A092520.

Sequence in context: A212180 A091050 A005361 * A322885 A292582 A008479

Adjacent sequences:  A303912 A303913 A303914 * A303916 A303917 A303918

KEYWORD

sign,easy,mult

AUTHOR

Werner Schulte, May 02 2018

STATUS

approved

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Last modified March 26 10:18 EDT 2019. Contains 321491 sequences. (Running on oeis4.)