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A259346 If n = 2^k then a(n) = 3^k, otherwise a(n) = 0.

%I A259346 #33 Sep 14 2023 02:31:14
%S A259346 1,3,0,9,0,0,0,27,0,0,0,0,0,0,0,81,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,243,
%T A259346 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,729,0,
%U A259346 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A259346 If n = 2^k then a(n) = 3^k, otherwise a(n) = 0.
%H A259346 Amiram Eldar, <a href="/A259346/b259346.txt">Table of n, a(n) for n = 1..10000</a>
%H A259346 Akhlesh Lakhtakia and Russell Messier, <a href="http://dx.doi.org/10.1016/0097-8493(89)90038-1">Self-similar sequences and chaos from Gauss sums</a>, Computers & Graphics, Vol. 13, No. 1 (1989), pp. 59-62. See Eq. (4a).
%H A259346 Akhlesh Lakhtakia and Russell Messier, <a href="/A005821/a005821.pdf">Self-similar sequences and chaos from Gauss sums</a>, Computers & Graphics, Vol. 13, No. 1 (1989), pp. 59-62 (Annotated scanned copy).
%F A259346 Completely multiplicative with a(2) = 3, a(p) = 0 for odd prime p. - _Andrew Howroyd_, Jul 27 2018
%F A259346 Dirichlet g.f.: 2^s/(2^s-3). - _Amiram Eldar_, Sep 14 2023
%t A259346 a[n_] := With[{k = IntegerExponent[n, 2]}, If[n == 2^k, 3^k, 0]];
%t A259346 Array[a, 85] (* _Jean-François Alcover_, Aug 27 2019 *)
%o A259346 (PARI) a(n)={my(e=valuation(n,2)); if(n == 2^e, 3^e, 0)} \\ _Andrew Howroyd_, Jul 27 2018
%K A259346 nonn,easy,mult
%O A259346 1,2
%A A259346 _N. J. A. Sloane_, Jun 27 2015
%E A259346 More terms from _Jon E. Schoenfield_, Jun 28 2015