A334657 Dirichlet g.f.: 1 / zeta(s-2).

1, -4, -9, 0, -25, 36, -49, 0, 0, 100, -121, 0, -169, 196, 225, 0, -289, 0, -361, 0, 441, 484, -529, 0, 0, 676, 0, 0, -841, -900, -961, 0, 1089, 1156, 1225, 0, -1369, 1444, 1521, 0, -1681, -1764, -1849, 0, 0, 2116, -2209, 0, 0, 0, 2601, 0, -2809, 0, 3025, 0, 3249, 3364, -3481, 0, -3721

Offset

1,2

Comments

Dirichlet inverse of A000290.

Moebius transform of A046970.

Inverse Moebius transform of A053822.

Links

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

Formula

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

a(1) = 1; a(n) = -n^2 * Sum_{d|n, d < n} a(d) / d^2.

a(n) = mu(n) * n^2.

Multiplicative with a(p^e) = -p^2 if e = 1 and 0 otherwise. - Amiram Eldar, Oct 25 2020

Mathematica

Table[MoebiusMu[n] n^2, {n, 61}]

Crossrefs

Cf. A008683, A055615, A334659, A334660.

Cf. A000290, A046970, A053822.

Sequence in context: A056584 A135245 A135244 * A364241 A011514 A238261

Adjacent sequences: A334654 A334655 A334656 * A334658 A334659 A334660

Keyword

sign,mult,easy

Author

Ilya Gutkovskiy, May 07 2020

Status

approved