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A355688
Dirichlet inverse of A354354, characteristic function of numbers that are neither multiples of 2 nor 3.
5
1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0
OFFSET
1
COMMENTS
Multiplicative because A354354 is.
LINKS
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
(PARI)
A354354(n) = ((n%2)&&(n%3));
memoA355688 = Map();
A355688(n) = if(1==n, 1, my(v); if(mapisdefined(memoA355688, n, &v), v, v = -sumdiv(n, d, if(d<n, A354354(n/d)*A355688(d), 0)); mapput(memoA355688, n, v); (v)));
(PARI) A355688(n) = (moebius(n)*A354354(n)); \\ Antti Karttunen, Dec 20 2022
CROSSREFS
Cf. also A355689, A355690.
Sequence in context: A104108 A267056 A089024 * A373154 A353488 A232991
KEYWORD
sign,mult
AUTHOR
Antti Karttunen, Jul 15 2022
STATUS
approved