A334659 Dirichlet g.f.: 1 / zeta(s-3).

1, -8, -27, 0, -125, 216, -343, 0, 0, 1000, -1331, 0, -2197, 2744, 3375, 0, -4913, 0, -6859, 0, 9261, 10648, -12167, 0, 0, 17576, 0, 0, -24389, -27000, -29791, 0, 35937, 39304, 42875, 0, -50653, 54872, 59319, 0, -68921, -74088, -79507, 0, 0, 97336, -103823, 0, 0, 0, 132651, 0, -148877

Offset: 1

Author

Ilya Gutkovskiy, May 07 2020

Keywords

• sign
• mult

Comments

Dirichlet inverse of A000578.

Moebius transform of A063453.

Inverse Moebius transform of A053825.

Links

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

Crossrefs

Cf. A008683, A055615, A334657, A334660.

Cf. A000578, A053825, A063453.

Programs

Mathematica

Table[MoebiusMu[n] n^3, {n, 53}]

Formula

G.f. A(x) satisfies: A(x) = x - 2^3 * A(x^2) - 3^3 * A(x^3) - 4^3 * A(x^4) - ...

a(1) = 1; a(n) = -n^3 * Sum_{d|n, d < n} a(d) / d^3.

a(n) = mu(n) * n^3.

Multiplicative with a(p^e) = -p^3 if e = 1 and 0 otherwise. - Amiram Eldar, Dec 05 2022