%I
%S 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 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 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N If n = 2^k then a(n) = 3^k, otherwise a(n) = 0.
%H Amiram Eldar, <a href="/A259346/b259346.txt">Table of n, a(n) for n = 1..10000</a>
%H Lakhtakia, Akhlesh and Russell Messier, <a href="http://dx.doi.org/10.1016/00978493(89)900381">Selfsimilar sequences and chaos from Gauss sums</a>, Computers & Graphics, Vol. 13, No. 1 (1989), pp. 5962. See Eq. (4a).
%H Lakhtakia, Akhlesh and Russell Messier, <a href="/A005821/a005821.pdf">Selfsimilar sequences and chaos from Gauss sums</a>, Computers & Graphics, Vol. 13, No. 1 (1989), pp. 5962 (Annotated scanned copy).
%F Completely multiplicative with a(2) = 3, a(p) = 0 for odd prime p.  _Andrew Howroyd_, Jul 27 2018
%t a[n_] := With[{k = IntegerExponent[n, 2]}, If[n == 2^k, 3^k, 0]];
%t Array[a, 85] (* _JeanFrançois Alcover_, Aug 27 2019 *)
%o (PARI) a(n)={my(e=valuation(n,2)); if(n == 2^e, 3^e, 0)} \\ _Andrew Howroyd_, Jul 27 2018
%K nonn,easy,mult
%O 1,2
%A _N. J. A. Sloane_, Jun 27 2015
%E More terms from _Jon E. Schoenfield_, Jun 28 2015
