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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.
7
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
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
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