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

1, 4, 7, 8, 9, 12, 15, 16, 17, 20, 23, 24, 25, 28, 31, 32, 33, 36, 39, 40, 41, 44, 47, 48, 49, 52, 55, 56, 57, 60, 63, 64, 65, 68, 71, 72, 73, 76, 79, 80, 81, 84, 87, 88, 89, 92, 95, 96, 97, 100, 103, 104, 105, 108, 111, 112, 113, 116, 119, 120, 121, 124, 127, 128, 129

Offset: 1

Author

Jon Perry, Sep 17 2002

Keywords

• nonn

Comments

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

Crossrefs

Essentially the same as A047538.

Programs

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)))))

Sage

[lucas_number1(n+2, 0, 1)+2*n for n in range(1, 66)] # Zerinvary Lajos, Mar 09 2009

Formula

From Paul Barry, Oct 27 2004: (Start)

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

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

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

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

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

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