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A074229 Numbers n such that Kronecker(6,n)==mu(gcd(6,n)). 2

%I

%S 1,5,19,23,25,29,43,47,49,53,67,71,73,77,91,95,97,101,115,119,121,125,

%T 139,143,145,149,163,167,169,173,187,191,193,197,211,215,217,221,235,

%U 239,241,245,259,263,265,269,283,287,289,293,307,311,313,317,331,335

%N Numbers n such that Kronecker(6,n)==mu(gcd(6,n)).

%H Colin Barker, <a href="/A074229/b074229.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).

%F From _Colin Barker_, Dec 14 2015: (Start)

%F a(n) = (3/2+(3*i)/2)*(i^n-i*(-i)^n)-(-1)^n+6*(n+1)-9 where i = sqrt(-1).

%F a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

%F G.f.: x*(1+4*x+14*x^2+4*x^3+x^4) / ((1-x)^2*(1+x)*(1+x^2)).

%F (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 (PARI) isok(n) = kronecker(6, n) == moebius(gcd(6, n)); \\ _Michel Marcus_, Mar 17 2014

%o (PARI) Vec(x*(1+4*x+14*x^2+4*x^3+x^4)/((1-x)^2*(1+x)*(1+x^2)) + O(x^100)) \\ _Colin Barker_, Dec 14 2015

%Y Equals 2 * A072065 + 1.

%K nonn,easy

%O 1,2

%A _Jon Perry_, Sep 17 2002

%E More terms from _Michel Marcus_, Mar 17 2014

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Last modified March 8 11:41 EST 2021. Contains 341948 sequences. (Running on oeis4.)