A390490 Dirichlet g.f.: (zeta(2*s))^2 / (zeta(s) * zeta(4*s)).

1, -1, -1, 2, -1, 1, -1, -2, 2, 1, -1, -2, -1, 1, 1, 2, -1, -2, -1, -2, 1, 1, -1, 2, 2, 1, -2, -2, -1, -1, -1, -2, 1, 1, 1, 4, -1, 1, 1, 2, -1, -1, -1, -2, -2, 1, -1, -2, 2, -2, 1, -2, -1, 2, 1, 2, 1, 1, -1, 2, -1, 1, -2, 2, 1, -1, -1, -2, 1, -1, -1, -4, -1, 1, -2, -2, 1, -1, -1, -2

Offset

1,4

Comments

Dirichlet inverse b(n) is multiplicative with b(p^e) = (-1)^floor(e/2) for prime p and e >= 0.

Signed version of A323308.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..10000

Formula

Multiplicative with a(p) = -1 and a(p^e) = 2 * (-1)^e for prime p and e > 1.

Dirichlet convolution of A323308 and A158522.

Dirichlet convolution with A000005 equals A365331.

Mathematica

f[p_, e_] := 2*(-1)^e; f[p_, 1] := -1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Nov 07 2025 *)

Prog

(PARI) lista(n) = direuler(p=2, n, (1-X)*(1-X^4)/(1-X^2)^2)

Crossrefs

Cf. A000005, A158522, A323308, A365331.

Sequence in context: A007424 A369163 A380398 * A323308 A365549 A278908

Adjacent sequences: A390487 A390488 A390489 * A390491 A390492 A390493

Keyword

sign,easy,mult

Author

Werner Schulte, Nov 07 2025

Status

approved