A156277 Dirichlet inverse of A011655, characteristic function of numbers that are not multiples of 3; Numbers appearing at every third row in the third column of A156241.

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

Offset

1

Comments

The Dirichlet inverse is A011655, and the Mobius inverse is represented by the absolute values of A154271. - R. J. Mathar, Jul 02 2013

From Antti Karttunen, Dec 31 2022: (Start)

Note the correspondences between four sequences:

A156277 --- abs ---> A359377

^ ^

| |

inv inv

| |

v v

A011655 <--- abs --- A359378

Here inv means that the sequences are Dirichlet Inverses of each other, and abs means taking absolute values.

(End)

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Formula

a(n) = -A008683(3n). - R. J. Mathar, Mar 31 2011

Dirichlet g.f.: 3^s/((3^s-1)*zeta(s)). - Amiram Eldar, Jan 07 2023

Maple

seq( -numtheory[mobius](3*n), n=1..80) ; # R. J. Mathar, Mar 31 2011

Prog

(PARI) A156277(n) = -moebius(3*n); \\ Antti Karttunen, Dec 29 2022

Crossrefs

Cf. A008683, A011655 (Dirichlet inverse), A154271, A156277, A359377 (absolute values), A359378 (Dirichlet inverse of the absolute values).

Cf. also A355689.

Sequence in context: A004585 A319448 A365428 * A359377 A353663 A260595

Adjacent sequences: A156274 A156275 A156276 * A156278 A156279 A156280

Keyword

easy,sign,mult

Author

Mats Granvik, Feb 07 2009

Extensions

Data section extended up to a(106) and a new primary definition (from R. J. Mathar's Jul 02 2013 comment) added to the name field by Antti Karttunen, Dec 29 2022

Status

approved