login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

A154271
Dirichlet inverse of A154272; Fully multiplicative with a(3^e) = (-1)^e, a(p^e) = 0 for primes p <> 3.
8
1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
OFFSET
1,1
COMMENTS
Abs(A154272) is a Fredholm-Rueppel-like sequence.
Sequence equals +1 if n is an even power of 3 (3^0, 3^2, 3^4,...), equals -1 if n is an odd power of 3 (3^1, 3^3, 3^5, 3^7,...) and zero elsewhere. - Comment edited by R. J. Mathar, Jun 24 2013
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..59049 (terms 1..220 from Mats Granvik)
FORMULA
Fully multiplicative with a(3) = -1, a(p) = 0 for primes p <> 3. - Antti Karttunen, Jul 24 2017
From Amiram Eldar, Nov 03 2023: (Start)
abs(a(n)) = A225569(n-1).
Dirichlet g.f.: 1/(1+3^(-s)). (End)
MATHEMATICA
nn = 95; a = PadRight[{1, 0, 1}, nn, 0]; Inverse[Table[Table[If[Mod[n, k] == 0, a[[n/k]], 0], {k, 1, nn}], {n, 1, nn}]][[All, 1]] (* Mats Granvik, Jul 24 2017 *)
PROG
(PARI) A154271(n) = { my(k=valuation(n, 3)); if((3^k)==n, (-1)^k, 0); }; \\ Antti Karttunen, Jul 24 2017
(Scheme) (define (A154271 n) (cond ((= 1 n) 1) ((zero? (modulo n 3)) (* -1 (A154271 (/ n 3)))) (else 0))) ;; Antti Karttunen, Jul 24 2017
CROSSREFS
Cf. A154272, A154269, A014578 (Möbius inverse), A154282, A225569.
Cf. A225569 (gives the absolute values when interpreted as the characteristic function of powers of 3, i.e., with starting offset 1 instead of 0).
Sequence in context: A015549 A015829 A016334 * A225569 A379480 A087032
KEYWORD
sign,mult,easy
AUTHOR
Mats Granvik, Jan 06 2009
EXTENSIONS
Alternative description added to the name by Antti Karttunen, Jul 24 2017
STATUS
approved