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

%I A130779 #50 Jan 01 2024 23:47:37
%S A130779 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,
%T A130779 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,
%U A130779 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
%N A130779 a(0)=a(1)=1, a(2)=2, a(n)=0 for n >= 3.
%C A130779 Inverse binomial transform of A002522. - _R. J. Mathar_, Jun 13 2008
%C A130779 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
%C A130779 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
%D A130779 J. Sándor and B. Crstici, Handbook of Number Theory II, Kluwer, 2004, p. 265.
%H A130779 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F A130779 G.f.: 1+x+2x^2.
%F A130779 a(n) = A167666(n,0). - _Philippe Deléham_, Feb 18 2012
%F A130779 a(n) = n! mod 3. - _Charles Kusniec_, Jan 25 2020
%t A130779 PadRight[{1,1,2},120,0] (* _Harvey P. Dale_, May 02 2015 *)
%t A130779 LinearRecurrence[{1},{1,1,2,0},105] (* _Ray Chandler_, Jul 15 2015 *)
%o A130779 (PARI) a(n)=if(n<3,max(n,1),0) \\ _Charles R Greathouse IV_, Dec 21 2011
%Y A130779 Cf. A002522, A007947, A130706, A167666.
%K A130779 nonn,mult,easy
%O A130779 0,3
%A A130779 _Paul Curtz_, Jul 14 2007