OFFSET
1
COMMENTS
Multiplicative because A354354 is.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..100000
FORMULA
a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A354354(n/d) * a(d).
a(n) = A008683(n) * A354354(n). [As the latter is fully multiplicative] - Antti Karttunen, Dec 20 2022
From Amiram Eldar, Dec 27 2022: (Start)
Multiplicative with a(p^e) = 0 if p <= 3 or e >= 2, and -1 otherwise.
Dirichlet g.f.: (2^s)*(3^s)/(zeta(s)*(2^s-1)*(3^s-1)). (End)
MATHEMATICA
a[n_] := If[GCD[n, 6] == 1, MoebiusMu[n], 0]; Array[a, 100] (* Amiram Eldar, Dec 27 2022 *)
PROG
CROSSREFS
KEYWORD
sign,mult
AUTHOR
Antti Karttunen, Jul 15 2022
STATUS
approved