A359819 Dirichlet inverse of A359590.

1, 0, -1, -1, -1, 0, -1, -1, 1, 0, -1, 1, -1, 0, 1, 1, -1, 0, -1, 1, 1, 0, -1, 1, 1, 0, -1, 1, -1, 0, -1, 1, 1, 0, 1, -1, -1, 0, 1, 1, -1, 0, -1, 1, -1, 0, -1, -1, 1, 0, 1, 1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, -1, -1, 1, 0, -1, 1, 1, 0, -1, -1, -1, 0, -1, 1, 1, 0, -1, -1, 1, 0, -1, -1, 1, 0, 1, 1, -1, 0, 1, 1, 1, 0, 1

Offset

1

Comments

Multiplicative because A359590 is.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A359590(n/d) * a(d).

Multiplicative with a(2) = 0, a(2^e) = -1 if e == 2 or 3 (mod 4) and 1 if e > 1 and e == 0 or 1 (mod 4), and for p > 2, a(p^e) = (-1)^e. - Amiram Eldar, Feb 09 2023

Mathematica

f[p_, e_] := (-1)^e; f[2, e_] := If[e==1, 0, If[Mod[e, 4] > 1, -1, 1]]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Feb 09 2023 *)

Crossrefs

Cf. A152822 (parity and the absolute values), A359590.

Sequence in context: A317198 A354993 A131379 * A284677 A191232 A267814

Adjacent sequences: A359816 A359817 A359818 * A359820 A359821 A359822

Keyword

sign,mult

Author

Antti Karttunen, Jan 17 2023

Status

approved