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A334659
Dirichlet g.f.: 1 / zeta(s-3).
6
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
1,2
COMMENTS
Dirichlet inverse of A000578.
Moebius transform of A063453.
Inverse Moebius transform of A053825.
LINKS
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
MATHEMATICA
Table[MoebiusMu[n] n^3, {n, 53}]
CROSSREFS
KEYWORD
sign,mult
AUTHOR
Ilya Gutkovskiy, May 07 2020
STATUS
approved