A130779 a(0)=a(1)=1, a(2)=2, a(n)=0 for n >= 3.

1, 1, 2, 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, 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

Offset: 0

Author

Paul Curtz, Jul 14 2007

Keywords

• nonn
• mult
• easy

Comments

Inverse binomial transform of A002522. - R. J. Mathar, Jun 13 2008

Multiplicative with a(2)=2, a(2^e)=0 if e>1, a(p^e)=0 for odd prime p if e>=1. Dirichlet g.f. 1+2^(1-s). - R. J. Mathar, Jun 28 2011

a(n-1) is the determinant of the symmetric n X n matrix M(i,j) = rad(gcd(i,j)) for 1 <= i, j <= n, where rad(n) is the largest squarefree number dividing n (A007947). - Amiram Eldar, Jul 19 2019

References

• J. Sándor and B. Crstici, Handbook of Number Theory II, Kluwer, 2004, p. 265.

Links

• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

Cf. A002522, A007947, A130706, A167666.

Programs

Mathematica

PadRight[{1,1,2},120,0] (* Harvey P. Dale, May 02 2015 *)
LinearRecurrence[{1},{1,1,2,0},105] (* Ray Chandler, Jul 15 2015 *)

PARI

a(n)=if(n<3,max(n,1),0) \\ Charles R Greathouse IV, Dec 21 2011

Formula

G.f.: 1+x+2x^2.

a(n) = A167666(n,0). - Philippe Deléham, Feb 18 2012

a(n) = n! mod 3. - Charles Kusniec, Jan 25 2020