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A361984
a(1) = 1, a(2) = 0; a(n) = Sum_{d|n, d < n} (-1)^(n/d) a(d).
3
1, 0, -1, 1, -1, 0, -1, 2, 0, 0, -1, -1, -1, 0, 1, 4, -1, 0, -1, -1, 1, 0, -1, -2, 0, 0, 0, -1, -1, 0, -1, 8, 1, 0, 1, 0, -1, 0, 1, -2, -1, 0, -1, -1, 0, 0, -1, -4, 0, 0, 1, -1, -1, 0, 1, -2, 1, 0, -1, 1, -1, 0, 0, 16, 1, 0, -1, -1, 1, 0, -1, 0, -1, 0, 0, -1, 1, 0, -1, -4, 0, 0, -1, 1, 1, 0, 1, -2, -1, 0, 1, -1, 1, 0, 1, -8, -1, 0, 0, 0
OFFSET
1,8
LINKS
FORMULA
a(n) is multiplicative with a(2) = 0, a(2^e) = 2^(e-2) if e>1. a(p) = -1, a(p^e) = 0 if e>1, p>2.
G.f. A(x) satisfies -x * (1 - x) = Sum_{k>=1} (-1)^k * A(x^k).
MATHEMATICA
f[p_, e_] := If[e == 1, -1, 0]; f[2, e_] := If[e == 1, 0, 2^(e-2)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, May 09 2023 *)
CROSSREFS
Partial sums give A309288.
Cf. A092673.
Sequence in context: A114643 A369055 A038498 * A319510 A257217 A184154
KEYWORD
sign,mult
AUTHOR
Seiichi Manyama, Apr 02 2023
STATUS
approved