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A332732
Dirichlet g.f.: zeta(6*s) / (zeta(s) * zeta(2*s) * zeta(3*s)).
2
1, -1, -1, -1, -1, 1, -1, 0, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 0, -1, 1, 0, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 0, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 0, 1, 0, 1, 1, -1, -1, -1, 1, 1, 0, 1, -1, -1, 1, 1, -1, -1, 0, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 0, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1
OFFSET
1
COMMENTS
Dirichlet inverse of A005361.
FORMULA
a(1) = 1; a(n) = -Sum_{d|n, d<n} A005361(n/d) * a(d).
a(n) = Sum_{d|n} A007427(n/d) * A299406(d).
Multiplicative with a(p^e) = A163810(e). - Amiram Eldar, Nov 30 2020
MATHEMATICA
a[1] = 1; a[n_] := -Sum[If[d < n, Times @@ (#[[2]] & /@ FactorInteger[n/d]) a[d], 0], {d, Divisors[n]}]; Table[a[n], {n, 1, 100}]
CROSSREFS
KEYWORD
sign,mult
AUTHOR
Ilya Gutkovskiy, Feb 21 2020
STATUS
approved