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. A225569 (gives the absolute values when interpreted as the characteristic function of powers of 3, i.e., with starting offset 1 instead of 0).
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