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

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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

N. J. A. Sloane, Jun 27 2015

Keywords

• nonn
• easy
• mult

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Akhlesh Lakhtakia and Russell Messier, Self-similar sequences and chaos from Gauss sums, Computers & Graphics, Vol. 13, No. 1 (1989), pp. 59-62. See Eq. (4a).
• Akhlesh Lakhtakia and Russell Messier, Self-similar sequences and chaos from Gauss sums, Computers & Graphics, Vol. 13, No. 1 (1989), pp. 59-62 (Annotated scanned copy).

Programs

Mathematica

a[n_] := With[{k = IntegerExponent[n, 2]}, If[n == 2^k, 3^k, 0]];
Array[a, 85] (* Jean-François Alcover, Aug 27 2019 *)

PARI

a(n)={my(e=valuation(n,2)); if(n == 2^e, 3^e, 0)} \\ Andrew Howroyd, Jul 27 2018

Formula

Completely multiplicative with a(2) = 3, a(p) = 0 for odd prime p. - Andrew Howroyd, Jul 27 2018

Dirichlet g.f.: 2^s/(2^s-3). - Amiram Eldar, Sep 14 2023

Extensions

More terms from Jon E. Schoenfield, Jun 28 2015