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A074231 Numbers n such that Kronecker(8,n) = mu(gcd(8,n)). 1

%I

%S 1,4,7,8,9,12,15,16,17,20,23,24,25,28,31,32,33,36,39,40,41,44,47,48,

%T 49,52,55,56,57,60,63,64,65,68,71,72,73,76,79,80,81,84,87,88,89,92,95,

%U 96,97,100,103,104,105,108,111,112,113,116,119,120,121,124,127,128,129

%N Numbers n such that Kronecker(8,n) = mu(gcd(8,n)).

%C A Chebyshev transform of (1+2x)/(1-2x) (A046055) given by G(x)->(1/(1+x^2))G(x/(1+x^2)). - _Paul Barry_, Oct 27 2004

%F From _Paul Barry_, Oct 27 2004: (Start)

%F G.f.: (1+x)^2/((1+x^2)*(1-2x+x^2));

%F e.g.f.: exp(x)(2+2x) - cos(x);

%F a(n) = 2n + 2 - cos(Pi*n/2);

%F a(n) = Sum_{k=0..n} (0^k + 4^k)*cos(Pi*(n-k)/2);

%F a(n) = Sum_{k=0..floor(n/2)} C(n-k, k)*(-1)^k(2*2^(n-2k)-0^(n-2k));

%F a(n) = 2a(n-1) - 2a(n-2) + 2a(n-3) - a(n-4). (End)

%o (PARI) for (x=1,200, for (y=1,200,if (kronecker(x,y)==moebius(gcd(x,y)),write("km.txt",x,";",y," : ",kronecker(x,y)))))

%o (Sage) [lucas_number1(n+2, 0, 1)+2*n for n in range(1, 66)] # _Zerinvary Lajos_, Mar 09 2009

%Y Essentially the same as A047538.

%K nonn

%O 1,2

%A _Jon Perry_, Sep 17 2002

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Last modified January 16 10:52 EST 2021. Contains 340206 sequences. (Running on oeis4.)